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    Wyświetlanie 1-52 z 52
    Tytuł:
    Existence results for random fractional differential equations
    Autorzy:
    Lupulescu, V.
    O’Regan, D.
    Rahman ur, G.
    Powiązania:
    https://bibliotekanauki.pl/articles/255930.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    random fractional differential equations
    fractional integral
    Caputo fractional derivative
    existence
    Opis:
    In this paper, an existence result for a random fractional differential equation is established under a Carathéodory condition. Existence results for extremal random solutions are also proved. Finally, an existence and uniqueness result is given.
    Źródło:
    Opuscula Mathematica; 2014, 34, 4; 813-825
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Boundary value problems for differential inclusions with fractional order
    Autorzy:
    Benchohra, Mouffak
    Hamani, Samira
    Powiązania:
    https://bibliotekanauki.pl/articles/729463.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    differential inclusion
    Caputo fractional derivative
    fractional integral
    existence
    fixed point
    Opis:
    In this paper, we shall establish sufficient conditions for the existence of solutions for a boundary value problem for fractional differential inclusions. Both cases of convex valued and nonconvex valued right hand sides are considered.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2008, 28, 1; 147-164
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Growth of solutions of a class of linear fractional differential equations with polynomial coefficients
    Autorzy:
    Hamouda, Saada
    Mahmoudi, Sofiane
    Powiązania:
    https://bibliotekanauki.pl/articles/2216191.pdf
    Data publikacji:
    2022
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    linear fractional differential equations
    growth of solutions
    Caputo fractional derivative operator
    Opis:
    This paper is devoted to the study of the growth of solutions of certain class of linear fractional differential equations with polynomial coefficients involving the Caputo fractional derivatives by using the generalized Wiman–Valiron theorem in the fractional calculus.
    Źródło:
    Opuscula Mathematica; 2022, 42, 3; 415-426
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional Integral Approximation and Caputo Derivatives with Modification of Trapezoidal Rule
    Autorzy:
    Pandiangan, Naomi
    Johar, Dwindi
    Purwani, Sri
    Powiązania:
    https://bibliotekanauki.pl/articles/1193326.pdf
    Data publikacji:
    2021
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Caputo fractional derivative
    Fractional integral
    Modified trapezoidal rule
    Rieman Liouville fractional integral
    Opis:
    In classical calculus, a function can be derived or integrated as many as natural numbers. Then a question arises regarding the fractional order of derivatives and integrals. There is a development of classical calculus called fractional calculus. Fractional calculus may be a department of science that amplifies the orders of derivatives and integrals into the order of rational numbers or even real numbers. The difficulty of finding solutions analytically for a complicated function of fractional integrals or fractional derivatives often occurs. In this paper, we will solve Rieman Liouville's fractional integral and Caputo's fractional derivative analytically using the trapezoidal rule modification method. Trapezoidal method is an approximation method that is resulted from the linear interpolation function. In this paper, we will find numerical simulations with modified trapezoidal method, to estimate some functions, and the results will be compared with previous research related to the Rieman Liouville fractional integral approximation and the Caputo fractional derivative. The result from simulation find that modified trapezoidal can approximate Caputo fractional derivative by replace α with -α and Quadratic schemes method is the best method to approximate Rieman Liouville fractional integral and Caputo fractional derivative.
    Źródło:
    World Scientific News; 2021, 153, 2; 169-180
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of solutions of the 1D fractional Cattaneo heat transfer equation
    Autorzy:
    Siedlecka, Urszula
    Ciesielski, Mariusz
    Powiązania:
    https://bibliotekanauki.pl/articles/2175501.pdf
    Data publikacji:
    2021
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    heat transfer
    Cattaneo equation
    fractional Caputo derivative
    Laplace transform
    Fourier transform
    wymiana ciepła
    równanie Cattaneo
    pochodna ułamkowa Caputo
    transformata Laplace'a
    transformata Fouriera
    Opis:
    In this paper, a solution of the single-phase lag heat conduction problem is presented. The research concerns the generalized 1D Cattaneo equation in a whole-space domain, where a second order time derivative is replaced by the fractional Caputo derivative. The Fourier-Laplace transform technique is used to determine a solution of the considered problem. The numerical inversion of the Laplace transforms is applied. The effect of the order of the fractional derivative on the temperature distribution is investigated.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 4; 87--98
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Axisymmetric solutions to the Cauchy problem for time-fractional diffusion equation in a circle
    Autorzy:
    Povstenko, Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/121736.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
    Tematy:
    Cauchy problem
    circle
    Caputo fractional derivative
    problem Cauchy'ego
    koło
    Opis:
    The Cauchy problems for time-fractional diffusion equation with delta pulse initial value of a sought-for function is studied in a circle domain in the axisymmetric case under zero Dirichlet and Neumann boundary conditions, respectively. The Caputo fractional derivative is used. The Laplace and finite Hankel integral transforms are employed. The results are illustrated graphically.
    Źródło:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2010, 15; 109-117
    2450-9302
    Pojawia się w:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Mittag-Leffler stability for a Timoshenko problem
    Autorzy:
    Tatar, Nasser-eddine
    Powiązania:
    https://bibliotekanauki.pl/articles/1838213.pdf
    Data publikacji:
    2021
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    Caputo fractional derivative
    Mittag-Leffler stability
    multiplier technique
    resolvent operator
    Opis:
    A Timoshenko system of a fractional order between zero and one is investigated here. Using a fractional version of resolvents, we establish an existence and uniqueness theorem in an appropriate space. Moreover, it is proved that lower order fractional terms (in the rotation component) are capable of stabilizing the system in a Mittag-Leffler fashion. Therefore, they deserve to be called damping terms. This is shown through the introduction of some new functionals and some fractional inequalities, and the establishment of some properties, involving fractional derivatives. In the case of different wave speeds of propagation we obtain convergence to zero.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2021, 31, 2; 219-232
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On a linear-quadratic problem with Caputo derivative
    Autorzy:
    Idczak, D.
    Walczak, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/254761.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    fractional Caputo derivative
    linear quadratic problem
    existence and uniqueness of a solution
    maximum principle
    gradient method
    projection of the gradient method
    Opis:
    In this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result and derive a maximum principle. Finally, we describe the gradient and projection of the gradient methods for the problem under consideration.
    Źródło:
    Opuscula Mathematica; 2016, 36, 1; 49-68
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence results for impulsive semilinear fractional differential inclusions with delay in Banach spaces
    Autorzy:
    Hammouche, Hadda
    Guerbati, Kaddour
    Benchohra, Mouffak
    Abada, Nadjat
    Powiązania:
    https://bibliotekanauki.pl/articles/729312.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    fractional calculus
    caputo fractional derivative
    multivalued map
    differential inclusions
    mild solution
    fixed point
    Opis:
    In this paper, we introduce a new concept of mild solution of some class of semilinear fractional differential inclusions of order 0 < α < 1. Also we establish an existence result when the multivalued function has convex values. The result is obtained upon the nonlinear alternative of Leray-Schauder type.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2013, 33, 2; 149-170
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On LQ optimization problem subject to fractional order irregular singular systems
    Autorzy:
    Muhafzan, -
    Nazra, Admi
    Yulianti, Lyra
    Zulakmal, -
    Revina, Refi
    Powiązania:
    https://bibliotekanauki.pl/articles/1409212.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    linear quadratic optimization
    fractional order
    irregular singular system
    Caputo fractional derivative
    Mittag-Leffler function
    Opis:
    In this paper we discuss the linear quadratic (LQ) optimization problem subject to fractional order irregular singular systems. The aim of this paper is to find the control-state pairs satisfying the dynamic constraint of the form a fractional order irregular singular systems such that the LQ objective functional is minimized. The method of solving is to convert such LQ optimization into the standard fractional LQ optimization problem. Under some particularly conditions we find the solution of the problem under consideration.
    Źródło:
    Archives of Control Sciences; 2020, 30, 4; 745-756
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A new numerical technique for solving fractional Bratu’s initial value problems in the Caputo and Caputo-Fabrizio sense
    Autorzy:
    Khalouta, Ali
    Kadem, Abdelouahab
    Powiązania:
    https://bibliotekanauki.pl/articles/1839797.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional Bratu’s initial value problem
    Caputo fractional derivative
    Caputo-Fabrizio fractional derivative
    natural transform method
    Adomian decomposition method
    ułamkowa pochodna Caputo
    ułamkowa pochodna Caputo-Fabrizio
    metoda transformacji naturalnej
    metoda dekompozycji Adomiana
    Opis:
    The purpose of this paper is to propose a new numerical technique called the natural decomposition method (NDM) for solving fractional Bratu’s initial value problems (FBIVP) in the Caputo and Caputo-Fabrizio sense. The NDM is a combined form of the natural transform method and the Adomian decomposition method. The numerical example is provided in order to validate the efficiency and reliability of the proposed method. The obtained results reveal that the proposed method is a very efficient and simple tool for solving fractional differential equations.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 43-56
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A new numerical technique for solving fractional Bratu’s initial value problems in the Caputo and Caputo-Fabrizio sense
    Autorzy:
    Khalouta, Ali
    Kadem, Abdelouahab
    Powiązania:
    https://bibliotekanauki.pl/articles/122619.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional Bratu’s initial value problem
    Caputo fractional derivative
    Caputo-Fabrizio fractional derivative
    natural transform method
    Adomian decomposition method
    ułamkowa pochodna Caputo
    ułamkowa pochodna Caputo-Fabrizio
    metoda transformacji naturalnej
    metoda dekompozycji Adomiana
    Opis:
    The purpose of this paper is to propose a new numerical technique called the natural decomposition method (NDM) for solving fractional Bratu’s initial value problems (FBIVP) in the Caputo and Caputo-Fabrizio sense. The NDM is a combined form of the natural transform method and the Adomian decomposition method. The numerical example is provided in order to validate the efficiency and reliability of the proposed method. The obtained results reveal that the proposed method is a very efficient and simple tool for solving fractional differential equations.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 43-56
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Boundary Value Problems for Differential Equations with Fractional Order and Nonlinear Integral Conditions
    Autorzy:
    Benchohra, Mouffak
    Hamani, Samira
    Powiązania:
    https://bibliotekanauki.pl/articles/746522.pdf
    Data publikacji:
    2009
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    boundary value problem
    Caputo fractional derivative
    fractional integral
    existence
    uniqueness
    fixed point
    integral conditions
    Opis:
    In this paper, we shall establish sufficient conditions for the existence of solutions for a class of boundary value problem for fractional differential equations involving the Caputo fractional derivative and nonlinear integral conditions.
    Źródło:
    Commentationes Mathematicae; 2009, 49, 2
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some closed form series solutions for the time-fractional diffusion-wave equation in polar coordinates with a generalized Caputo fractional derivative
    Autorzy:
    Elkott, Ibrahim
    Abdel-Latif, Mohamed S.
    El-Kalla, Ibrahim L.
    Abdel Kader, Abass H.
    Powiązania:
    https://bibliotekanauki.pl/articles/24201502.pdf
    Data publikacji:
    2023
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    generalized time-fractional Caputo derivative
    generalized Laplace transform
    Hankel transform
    diffusion-wave equation
    uogólniona ułamkowa pochodna Caputo w czasie
    uogólniona transformata Laplace'a
    transformata Hankela
    równanie fali dyfuzyjnej
    Opis:
    In this paper, we obtain some closed form series solutions for the time fractional diffusion-wave equation (TFDWE) with the generalized time-fractional Caputo derivative (GTFCD) associated with a source term in polar coordinates. These solutions are found using generalized Laplace and Hankel transforms. We obtained the closed form series solutions in the form of the Polygamma function. The effect of the fractional order derivative on the diffusion-wave variable is illustrated graphically.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2023, 22, 2; 5--14
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An analytical solution to the problem of time-fractional heat conduction in a composite sphere
    Autorzy:
    Kukla, S.
    Siedlecka, U.
    Powiązania:
    https://bibliotekanauki.pl/articles/202020.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    heat conduction
    multilayered sphere
    Caputo fractional derivative
    przewodzenie ciepła
    powłoka wielowarstwowa
    pochodna ułamkowego rzędu Caputo
    Opis:
    An analytical solution to the problem of time-fractional heat conduction in a sphere consisting of an inner solid sphere and concentric spherical layers is presented. In the heat conduction equation, the Caputo time-derivative of fractional order and the Robin boundary condition at the outer surface of the sphere are assumed. The spherical layers are characterized by different material properties and perfect thermal contact is assumed between the layers. The analytical solution to the problem of heat conduction in the sphere for time-dependent surrounding temperature and for time-space-dependent volumetric heat source is derived. Numerical examples are presented to show the effect of the harmonically varying intensity of the heat source and the harmonically varying surrounding temperature on the temperature in the sphere for different orders of the Caputo time-derivative.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2017, 65, 2; 179-186
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On fractional random differential equations with delay
    Autorzy:
    Vu, H.
    Phung, N. N.
    Phuong, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/254723.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    sample path fractional integral
    sample path fractional derivative
    fractional differential equations
    sample fractional random differential equations
    Caputo fractional derivative
    delay
    Opis:
    In this paper, we consider the existence and uniqueness of solutions of the fractional random differential equations with delay. Moreover, some kind of boundedness of the solution is proven. Finally, the applicability of the theoretical results is illustrated with some real world examples.
    Źródło:
    Opuscula Mathematica; 2016, 36, 4; 541-556
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Weak solutions for nonlinear fractional differential equations with integral boundary conditions in Banach spaces
    Autorzy:
    Benchohra, M.
    Mostefai, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/255390.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    boundary value problem
    Caputo fractional derivative
    measure of weak noncompactness
    Pettis integrals
    weak solution
    Opis:
    The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.
    Źródło:
    Opuscula Mathematica; 2012, 32, 1; 31-40
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Distributed optimal control problems driven by space-time fractional parabolic equations
    Autorzy:
    Mehandiratta, Vaibhav
    Mehra, Mani
    Leugering, Günter
    Powiązania:
    https://bibliotekanauki.pl/articles/2183495.pdf
    Data publikacji:
    2022
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    space-time fractional parabolic equations
    Caputo fractional derivative
    distributed control
    L1 method
    Grünwald-Letnikov formula
    Opis:
    We study distributed optimal control problems, governed by space-time fractional parabolic equations (STFPEs) involving time-fractional Caputo derivatives and spatial fractional derivatives of Sturm-Liouville type. We first prove existence and uniqueness of solutions of STFPEs on an open bounded interval and study their regularity. Then we show existence and uniqueness of solutions to a quadratic distributed optimal control problem. We derive an adjoint problem using the right-Caputo derivative in time and provide optimality conditions for the control problem. Moreover, we propose a finite difference scheme to find the approximate solution of the considered optimal control problem. In the proposed scheme, the well-known L1 method has been used to approximate the time-fractional Caputo derivative, while the spatial derivative is approximated using the Grünwald-Letnikov formula. Finally, we demonstrate the accuracy and the performance of the proposed difference scheme via examples.
    Źródło:
    Control and Cybernetics; 2022, 51, 2; 191--226
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and stability analysis of nonlinear sequential coupled system of Caputo fractional differential equations with integral boundary conditions
    Autorzy:
    Zada, Akbar
    Yar, Muhammad
    Li, Tongxing
    Powiązania:
    https://bibliotekanauki.pl/articles/744661.pdf
    Data publikacji:
    2018
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    Caputo fractional derivative
    Riemann–Liouville fractional integral
    coupled system
    existence
    uniqueness
    fixed point theorem
    Hyers–Ulam stability
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica; 2018, 17
    2300-133X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional integro-differential inclusions with state-dependent delay
    Autorzy:
    Aissani, Khalida
    Benchohra, Mouffak
    Ezzinbi, Khalil
    Powiązania:
    https://bibliotekanauki.pl/articles/729499.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    fractional integro-differential inclusions
    Caputo fractional derivative
    mild solution
    multivalued map
    Bohnenblust-Karlin's fixed point
    state-dependent delay
    Opis:
    In this paper, we establish sufficient conditions for the existence of mild solutions for fractional integro-differential inclusions with state-dependent delay. The techniques rely on fractional calculus, multivalued mapping on a bounded set and Bohnenblust-Karlin's fixed point theorem. Finally, we present an example to illustrate the theory.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2014, 34, 2; 153-167
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Application of LDG scheme to solve semi-differential equations
    Autorzy:
    Izadi, Mohammad
    Powiązania:
    https://bibliotekanauki.pl/articles/122346.pdf
    Data publikacji:
    2019
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    Caputo fractional derivative
    local discontinuous Galerkin method
    semi-differential equations
    pochodna ułamkowa Caputo
    nieciągła metoda Galerkina
    schemat LDG
    równania różnicowe
    Opis:
    In the current work, we investigate a technique based on discontinuous Galerkin method for the numerical approximation of semi-differential equations with Caputo’s fractional derivative. In this approach, using the natural upwind fluxes enables us to solve the model problem element by element locally in each subintervals and there is no need to solve a full global matrix. Numerical experiments are given to verify the efficiency and accuracy of the proposed method. Numerical solutions are compared with the exact solutions as well as the numerical solutions obtained by other available well-established computational procedures. The results show that the LDG method is more accurate for solving this class of differential equation with relatively low degrees of polynomials and number of elements.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 4; 27-39
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A New Class of Fractional Cumulative Residual Entropy - Some Theoretical Results
    Autorzy:
    Benmahmoud, Slimane
    Powiązania:
    https://bibliotekanauki.pl/articles/2200956.pdf
    Data publikacji:
    2023
    Wydawca:
    Instytut Łączności - Państwowy Instytut Badawczy
    Tematy:
    cumulative residual entropy (CRE)
    entropy’s generating function
    fractional calculus
    information measure
    Riemann-Liouville/Caputo fractional integral
    Riemann-Liouville/Caputo fractional derivative
    Tsallis/Rényi entropy
    Opis:
    In this paper, by differentiating the entropy’s generating function (i.e., h(t) = R SX̄F tX (x)dx) using a Caputo fractional-order derivative, we derive a generalized non-logarithmic fractional cumulative residual entropy (FCRE). When the order of differentiation α → 1, the ordinary Rao CRE is recovered, which corresponds to the results from first-order ordinary differentiation. Some properties and examples of the proposed FCRE are also presented.
    Źródło:
    Journal of Telecommunications and Information Technology; 2023, 1; 25--29
    1509-4553
    1899-8852
    Pojawia się w:
    Journal of Telecommunications and Information Technology
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analytical solution of a fractional model of fluid flow through narrowing system in terms of Mittag-Leffler function
    Autorzy:
    Choudhary, A.
    Kumar, D.
    Singh, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/264897.pdf
    Data publikacji:
    2020
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    transformata Hankela
    funkcja Bessela
    pochodna Caputo
    narrowing system
    generalized Caputo fractional derivative
    Sumudu transform
    finite Hankel transform
    Bessel function
    Mittag-Leffler function
    Opis:
    In this work, we discuss a fractional model of a flow equation in a simple pipeline. Pipeline narrowing is a crucial aspect in drinking water distribution processes, sewage system and in oil-well schemes. The solution of the mathematical model is determined with the aid of the Sumudu transform and finite Hankel transform. The results derived in the current study are in compact and graceful forms in terms of the Mittag-Leffler type function, which are convenient for numerical and theoretical evaluation.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2020, 25, 1; 1-11
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional order impulsive partial hyperbolic differential inclusions with variable times
    Autorzy:
    Abbas, Saïd
    Benchohra, Mouffak
    Górniewicz, Lech
    Powiązania:
    https://bibliotekanauki.pl/articles/729238.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    impulsive functional differential inclusions
    fractional order
    solution
    left-sided mixed Riemann-Liouville integral
    Caputo fractional-order derivative
    variable times
    fixed point
    Opis:
    This paper deals with the existence of solutions to some classes of partial impulsive hyperbolic differential inclusions with variable times involving the Caputo fractional derivative. Our works will be considered by using the nonlinear alternative of Leray-Schauder type.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2011, 31, 1; 91-114
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Dirichlet problem for the time-fractional advection-diffusion equation in a half-space
    Autorzy:
    Povstenko, Y.
    Klekot, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/122941.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    Caputo fractional derivative
    advection-diffusion equation
    Laplace integral transform
    Fourier sine transform
    Mittag-Leffler function
    pochodna rzędu ułamkowego Caputo
    funkcja Mittag-Lefflera
    Opis:
    The one-dimensional time-fractional advection-diffusion equation with the Caputo time derivative is considered in a half-space. The fundamental solution to the Dirichlet problem and the solution of the problem with constant boundary condition are obtained using the integral transform technique. The numerical results are illustrated graphically.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 2; 73-83
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Impulsive Hyperbolic System of Partial Differential Equations of Fractional Order with Delay
    Autorzy:
    Benchohra, Mouffak
    Boutefal, Zohra
    Powiązania:
    https://bibliotekanauki.pl/articles/746465.pdf
    Data publikacji:
    2014
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    impulsive partial hyperbolic differential equations,
    fractional order, solution
    left-sided mixed Riemann-Liouville integral
    Caputo fractional-order derivative
    finite delay
    fixed point
    Opis:
    This paper deals with the existence of solutions to impulsive partial hyperbolic differential equations with finite delay, involving the Caputo fractional derivative. Our results will be obtained using Krasnoselskii fixed point theorem.
    Źródło:
    Commentationes Mathematicae; 2014, 54, 2
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The method of upper and lower solutions for partial hyperbolic fractional order differential inclusions with impulses
    Autorzy:
    Abbas, Saïd
    Benchohra, Mouffak
    Powiązania:
    https://bibliotekanauki.pl/articles/729279.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    impulsive hyperbolic differential inclusion
    fractional order
    upper solution
    lower solution
    left-sided mixed Riemann-Liouville integral
    Caputo fractional-order derivative
    fixed point
    Opis:
    In this paper we use the upper and lower solutions method to investigate the existence of solutions of a class of impulsive partial hyperbolic differential inclusions at fixed moments of impulse involving the Caputo fractional derivative. These results are obtained upon suitable fixed point theorems.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2010, 30, 1; 141-161
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Generalized Differential Transform Method for solution of a free vibration linear differential equation with fractional derivative damping
    Autorzy:
    Das, Deepanjan
    Powiązania:
    https://bibliotekanauki.pl/articles/122961.pdf
    Data publikacji:
    2019
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional differential equations
    Caputo fractional derivative
    generalized
    differential transform method
    analytic solution
    ułamkowe równania różniczkowe
    ułamkowa pochodna Caputo
    metoda transformacji różnicowej
    rozwiązanie analityczne
    ułamkowe równanie różniczkowe
    Opis:
    In the present paper, the Generalized Differential Transform Method (GDTM) is used for obtaining the approximate analytic solutions of a free vibration linear differential equation of a single-degree-of-freedom (SDOF) system with fractional derivative damping. The fractional derivatives are described in the Caputo sense.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 2; 19-29
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and convergence results for Caputo fractional Volterra integro-differential equations
    Autorzy:
    Hamoud, A. A.
    Bani Issa, M. Sh.
    Ghadle, K. P.
    Abdulghani, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/2052432.pdf
    Data publikacji:
    2018
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    homotopy analysis method
    Caputo fractional derivative
    Volterra integro-differential equation
    approximate solution
    homotopijna metoda analizy
    pochodna ułamkowa Caputo
    równanie różniczkowe Volterry
    rozwiązanie przybliżone
    Opis:
    In this article, homotopy analysis method is successfully applied to find the approximate solution of Caputo fractional Volterra integro-differential equation. The reliability of the method and reduction in the size of the computational work give this method a wider applicability. Also, the behavior of the solution can be formally determined by analytical approximate. Moreover, we proved the existence and convergence of the solution. Finally, an example is included to demonstrate the validity and applicability of the proposed technique.
    Źródło:
    Journal of Mathematics and Applications; 2018, 41; 109-121
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Extremal solutions to a coupled system of nonlinear fractional differential equations with Caputo fractional derivatives
    Autorzy:
    Derbazi, Choukri
    Baitiche, Zidane
    Benchohra, Mouffak
    Graef, John R.
    Powiązania:
    https://bibliotekanauki.pl/articles/2052385.pdf
    Data publikacji:
    2021
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    Caputo fractional derivative
    coupled system
    extremal solutions
    monotone iterative technique
    upper and lower solutions
    pochodna ułamkowa Caputo
    system sprzężony
    ekstremalne rozwiązania
    monotoniczna technika iteracyjna
    Opis:
    Using the well-known monotone iterative technique together with the method of upper and lower solutions, the authors investigate the existence of extremal solutions to a class of coupled systems of nonlinear fractional differential equations involving the $\psi$-Caputo derivative with initial conditions. As applications of this work, two illustrative examples are presented.
    Źródło:
    Journal of Mathematics and Applications; 2021, 44; 19-34
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonlinear fractional differential equations with non-instantaneous impulses in Banach spaces
    Autorzy:
    Benchohra, M.
    Slimane, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/2052426.pdf
    Data publikacji:
    2018
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    initial value problem
    impulses
    Caputo fractional derivative
    measure of noncompactness
    fixed point
    Banach space
    wartość początkowa
    impulsy
    pochodna ułamkowa Caputo
    miara braku zgodności
    punkt stały
    przestrzeń Banacha
    Opis:
    This paper is devoted to study the existence of solutions for a class of initial value problems for non-instantaneous impulsive fractional differential equations involving the Caputo fractional derivative in a Banach space. The arguments are based upon Monch's fixed point theorem and the technique of measures of noncompactness.
    Źródło:
    Journal of Mathematics and Applications; 2018, 41; 39-51
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some new existence results and stability concepts for fractional partial random differential equations
    Autorzy:
    Abbas, S.
    Benchohra, M.
    Darwish, M. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/357770.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    random differential equations
    left-sided mixed Riemann-Liouville integral
    Caputo fractional-order derivative
    Banach space
    Darboux problem
    Ulam stability
    równanie różniczkowe
    pochodna Caputo
    przestrzeń Banacha
    problem Darbouxa
    Opis:
    In the present paper we provide some existence results and Ulam’s type stability concepts for the Darboux problem of partial fractional random differential equations in Banach spaces, by applying the measure of noncompactness and a random fixed point theorem with stochastic domain.
    Źródło:
    Journal of Mathematics and Applications; 2016, 39; 5-22
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On theoretical and practical aspects of Duhamel’s integral
    Autorzy:
    Różański, Michał
    Sikora, Beata
    Smuda, Adrian
    Wituła, Roman
    Powiązania:
    https://bibliotekanauki.pl/articles/2083463.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    Duhamel’s integral
    Duhamel’s principle
    Duhamel’s formula
    Laplace transformation
    semigroup of operators
    Leibniz integral rule
    Volterra integral equation
    Caputo fractional derivative
    Opis:
    The paper is a new approach to the Duhamel integral. It contains an overview of formulas and applications of Duhamel’s integral as well as a number of new results on the Duhamel integral and principle. Basic definitions are recalled and formulas for Duhamel’s integral are derived via Laplace transformation and Leibniz integral rule. Applications of Duhamel’s integral for solving certain types of differential and integral equations are presented. Moreover, an interpretation of Duhamel’s formula in the theory of operator semigroups is given. Some applications of Duhamel’s formula in control systems analysis are discussed. The work is also devoted to the usage of Duhamel’s integral for differential equations with fractional order derivative.
    Źródło:
    Archives of Control Sciences; 2021, 31, 4; 815-847
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses
    Autorzy:
    Abbas, Saïd
    Benchohra, Mouffak
    Abdalla Darwish, Mohamed
    Powiązania:
    https://bibliotekanauki.pl/articles/729578.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    fractional differential inclusion
    left-sided mixed Riemann-Liouville integral
    Caputo fractional order derivative
    upper solution
    lower solution
    extremal solution
    fixed point
    Banach algebras
    not instantaneous impulses
    Opis:
    In this paper, we use the upper and lower solutions method combined with a fixed point theorem for multivalued maps in Banach algebras due to Dhage for investigations of the existence of solutions of a class of discontinuous partial differential inclusions with not instantaneous impulses. Also, we study the existence of extremal solutions under Lipschitz, Carath´eodory and certain monotonicity conditions
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2016, 36, 2; 155-179
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A new modification of the reduced differential transform method for nonlinear fractional partial differential equations
    Autorzy:
    Khalouta, Ali
    Kadem, Abdelouahab
    Powiązania:
    https://bibliotekanauki.pl/articles/1839758.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    nonlinear fractional partial differential equations
    Caputo fractional derivative
    Shehu transform method
    reduced differential transform method
    approximate analytical solution
    nieliniowe równania różniczkowe cząstkowe ułamkowe
    pochodna ułamkowa Caputo
    metoda transformacji Shehu
    metoda transformacji różnicowej
    Opis:
    The objective of this study is to present a new modification of the reduced differential transform method (MRDTM) to find an approximate analytical solution of a certain class of nonlinear fractional partial differential equations in particular, nonlinear time-fractional wave-like equations with variable coefficients. This method is a combination of two different methods: the Shehu transform method and the reduced differential transform method. The advantage of the MRDTM is to find the solution without discretization, linearization or restrictive assumptions. Three different examples are presented to demonstrate the applicability and effectiveness of the MRDTM. The numerical results show that the proposed modification is very effective and simple for solving nonlinear fractional partial differential equations.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 3; 45-58
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical solution of a fractional coupled system with the Caputo-Fabrizio fractional derivative
    Autorzy:
    Mansouri, Ikram
    Bekkouche, Mohammed Moumen
    Ahmed, Abdelaziz Azeb
    Powiązania:
    https://bibliotekanauki.pl/articles/2202061.pdf
    Data publikacji:
    2023
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    Caputo-Fabrizio fractional derivative
    fractional integral
    coupled system
    fractional differential equation
    fixed point
    Adomian decomposition method
    pochodna ułamkowa Caputo-Fabrizio
    całkowanie ułamkowe
    system sprzężony
    ułamkowe równanie różniczkowe
    punkt stały
    metoda dekompozycji Adomiana
    Opis:
    Within this work, we discuss the existence of solutions for a coupled system of linear fractional differential equations involving Caputo-Fabrizio fractional orders. We prove the existence and uniqueness of the solution by using the Picard-Lindel ̈of method and fixed point theory. Also, to compute an approximate solution of problem, we utilize the Adomian decomposition method (ADM), as this method provides the solution in the form of a series such that the infinite series converge to the exact solution. Numerical examples are presented to illustrate the validity and effectiveness of the proposed method.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2023, 22, 1; 46--56
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Generalized Isoperimetric FVPs Via Caputo Approach
    Autorzy:
    Taïeb, Amele
    Dahmani, Zoubir
    Powiązania:
    https://bibliotekanauki.pl/articles/2188101.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
    Tematy:
    Caputo derivative
    Fractional calculus of variations
    isoperimetric problems
    Opis:
    In this paper, we study several fractional variational problems with functionals that contain n unknown functions with their higher order Caputo derivatives and Riemann–Liouville integrals. We prove generalized fractional Euler–Lagrange equations. We also study an isoperimetric problem with multiple constraints, and we find the optimality conditions. Some examples are provided to illustrate the applications of the results.
    Źródło:
    Universitatis Iagellonicae Acta Mathematica; 2019, 56; 23-40
    2084-3828
    0083-4386
    Pojawia się w:
    Universitatis Iagellonicae Acta Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of fractional electrical circuit with sinusoidal input signal using Caputo and conformable derivative definitions
    Autorzy:
    Piotrowska, Ewa
    Powiązania:
    https://bibliotekanauki.pl/articles/378130.pdf
    Data publikacji:
    2019
    Wydawca:
    Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
    Tematy:
    fractional order system
    Sinusoidal Signals
    Caputo definition
    conformable fractional derivative definition
    fractional electrical circuit
    Opis:
    This paper presents the fractional electrical circuit in the transient state described by the fractional-order state-space equations. General solutions to the fractional state-space equations containing two types of definitions of fractional derivative: Caputo definition and the conformable fractional derivative definition are given the solutions in the case of: 1) control in the form of sine function at zero initial states 2) control in the form of cosine function at zero initial states 3) control in the form of the sine function with phase shift at zero initial states. The solutions are shown for capacitor voltages for fractional derivative orders of 0.7; 0.8; 1.0. The results were compared using graphs.
    Źródło:
    Poznan University of Technology Academic Journals. Electrical Engineering; 2019, 97; 155-167
    1897-0737
    Pojawia się w:
    Poznan University of Technology Academic Journals. Electrical Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The fundamental solutions to the central symmetric time-fractional heat conduction equation with heat absorption
    Autorzy:
    Povstenko, Y.
    Klekot, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/122778.pdf
    Data publikacji:
    2017
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    non-Fourier heat conduction
    Caputo fractional derivative
    heat absorption
    Laplace integral transform
    Fourier transform
    Mittag-Leffler function
    przewodzenie ciepła
    pochodna ułamkowa Caputo
    absorpcja ciepła
    transformata Laplace'a
    transformata Fouriera
    funkcja Mittag-Lefflera
    Opis:
    The time-fractional heat conduction equation with heat absorption proportional to temperature is considered in the case of central symmetry. The fundamental solutions to the Cauchy problem and to the source problem are obtained using the integral transform technique. The numerical results are presented graphically.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2017, 16, 2; 101-112
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On controllability of fractional positive continuous-time linear systems with delay
    Autorzy:
    Sikora, Beata
    Matlok, Natalia
    Powiązania:
    https://bibliotekanauki.pl/articles/1409030.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional systems
    positive systems
    Caputo derivative
    controllability
    delay
    Metzler matrix
    Opis:
    In the paper positive fractional continuous-time linear systems are considered. Positive fractional systems without delays and positive fractional systems with a single delay in control are studied. New criteria for approximate and exact controllability of systems without delays as well as a relative controllability criterion of systems with delay are established and proved. Numerical examples are presented for different controllability criteria. A practical application is proposed.
    Źródło:
    Archives of Control Sciences; 2021, 31, 1; 29-51
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Heat conduction in a finite medium using the fractional single-phase-lag model
    Autorzy:
    Siedlecka, Urszula
    Powiązania:
    https://bibliotekanauki.pl/articles/200748.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    single-phase-lagging heat conduction
    Caputo derivative
    fractional heat conduction
    przewodzenie ciepła
    Pochodna Caputo
    Opis:
    In the paper, a solution of the time-fractional single-phase-lagging heat conduction problem in finite regions is presented. The heat conduction equation with the Caputo time-derivative is complemented by the Robin boundary conditions. The Laplace transform with respect to the time variable and an expansion in the eigenfunctions series with respect to the space variable was applied. A method for the numerical inversion of the Laplace transforms was used. Formulation and solution of the problem cover the heat conduction in a finite slab, hollow cylinder and hollow sphere. The effect of the fractional order of the Caputo derivative and the phase-lag parameter on the temperature distribution in a slab has been numerically investigated.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2019, 67, 2; 401-407
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Problems with modeling of fractional electrical circuits containing supercapacitors
    Autorzy:
    Piotrowska, Ewa
    Powiązania:
    https://bibliotekanauki.pl/articles/378115.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
    Tematy:
    fractional order system
    electrical circuits containing supercapacitors
    Caputo definition
    Conformable Fractional Derivative definition
    Opis:
    For proper operation, diagnostics or control, it is required to know the parameters of the supercapacitor replacement model (relationship between current and voltage at the terminals). The paper describe the bahavior of the eletrical circuit (RC) containing the supercapacitor were used the fractional derivatives of Caputo definiton and Conformable Fractional Derivative definition. Verification of the correctness of the suggested electrical circuit models was carried out a series of measurements of the system response to the given control signal. The measurement data were compared by fractionalorder derivatives: classical case, Caputo definition and CFD definition. Conducting a series of experiments with charging a supercapacitor in an RC circuit, constant control voltage from 2 V to 5 V with an exchanged external resistor, it was shown that none of the three mathematical models reflects the real behavior of the supercapacitor. It has been shown that the behavior of supercapacitor requires the use of different mathematical than fractional derivatives.
    Źródło:
    Poznan University of Technology Academic Journals. Electrical Engineering; 2020, 104; 65-74
    1897-0737
    Pojawia się w:
    Poznan University of Technology Academic Journals. Electrical Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the asymptotic behavior of nonoscillatory solutions of certain fractional differential equations with positive and negative terms
    Autorzy:
    Graef, John R.
    Grace, Said R.
    Tune, Ercan
    Powiązania:
    https://bibliotekanauki.pl/articles/255164.pdf
    Data publikacji:
    2020
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    integro-differential equations fractional differential equations nonoscillatory solutions boundedness
    Caputo derivative
    Opis:
    This paper is concerned with the asymptotic behavior of the nonoscillatory solutions of the forced fractional differential equation with positive and negative terms of the form [formula] where t ≥ c ≥ α ∈(0, 1), η ≥ 1 is the ratio of positive odd integers, and [formula] denotes the Caputo fractional derivative of y of order α. The cases [formula] are considered. The approach taken here can be applied to other related fractional differential equations. Examples are provided to illustrate the relevance of the results obtained.
    Źródło:
    Opuscula Mathematica; 2020, 40, 2; 227-239
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Different kinds of boundary conditions for time-fractional heat conduction equation
    Autorzy:
    Povstenko, Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/121936.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
    Tematy:
    boundary conditions
    heat conduction
    time-fractional equation
    Caputo derivative
    przewodzenie ciepła
    warunki brzegowe
    pochodna Caputo
    Opis:
    The time-fractional heat conduction equation with the Caputo derivative of the order 0 ˂ α ˂ 2 is considered in a bounded domain. For this equation different types of boundary conditions can be given. The Dirichlet boundary condition prescribes the temperature over the surface of the body. In the case of mathematical Neumann boundary condition the boundary values of the normal derivative are set, the physical Neumann boundary condition specifies the boundary values of the heat flux. In the case of the classical heat conduction equation (α = 1), these two types of boundary conditions are identical, but for fractional heat conduction they are essentially different. The mathematical Robin boundary condition is a specification of a linear combination of the values of temperature and the values of its normal derivative at the boundary of the domain, while the physical Robin boundary condition prescribes a linear combination of the values of temperature and the values of the heat flux at the surface of a body.
    Źródło:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2011, 16; 61-66
    2450-9302
    Pojawia się w:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Application of fractional order theory of thermoelasticity in an elliptical disk and associated thermal stresses
    Autorzy:
    Thakare, S.
    Panke, Y.
    Hadke, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/1839826.pdf
    Data publikacji:
    2020
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    naprężenia termiczne
    pochodna Caputo
    termosprężystość
    elliptical disk
    fractional order theory
    Caputo derivative
    integral transform
    thermal stresses
    thermal deflection
    Opis:
    In this article, a time fractional-order theory of thermoelasticity is applied to an isotropic homogeneous elliptical disk. The lower and upper surfaces of the disk are maintained at zero temperature, whereas the sectional heat supply is applied on the outer curved surface. Thermal deflection and associated thermal stresses are obtained in terms of Mathieu function of the first kind of order 2n. Numerical evaluation is carried out for the temperature distribution, Thermal deflection and thermal stresses and results of the resulting quantities are depicted graphically.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2020, 25, 3; 169-180
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Results on the controllability of Caputo’s fractional descriptor systems with constant delays
    Autorzy:
    Beata, Sikora
    Powiązania:
    https://bibliotekanauki.pl/articles/27311455.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    descriptor systems
    fractional-order systems
    Caputo derivative
    Drazin inverse
    controllability
    pochodna Caputo
    odwrotność Drazina
    sterowalność
    system deskryptorowy
    system ułamkowego rzędu
    Opis:
    The paper investigates the controllability of fractional descriptor linear systems with constant delays in control. The Caputo fractional derivative is considered. Using the Drazin inverse and the Laplace transform, a formula for solving of the matrix state equation is obtained. New criteria of relative controllability for Caputo’s fractional descriptor systems are formulated and proved. Both constrained and unconstrained controls are considered. To emphasize the importance of the theoretical studies, an application to electrical circuits is presented as a practical example.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 4; art. no. e146287
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analytical and numerical study for a fractional boundary value problem with a conformable fractional derivative of Caputo and its fractional integral
    Autorzy:
    Bekkouche, M. Moumen
    Guebbai, H.
    Powiązania:
    https://bibliotekanauki.pl/articles/1839786.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional boundary value problem
    Volterra-Fredholm integral equation
    fractional derivative
    fractional integral
    równanie całkowe Volterry-Fredholma
    ułamkowa wartość brzegowa
    pochodna ułamkowa Caputo
    Opis:
    We study the existence and uniqueness of the solution of a fractional boundary value problem with conformable fractional derivation of the Caputo type, which increases the interest of this study. In order to study this problem we have introduced a new definition of fractional integral as an inverse of the conformable fractional derivative of Caputo, therefore, the proofs are based upon the reduction of the problem to a equivalent linear Volterra-Fredholm integral equations of the second kind, and we have built the minimum conditions to obtain the existence and uniqueness of this solution. The analytical study is followed by a complete numerical study.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 2; 31-42
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Controllability criteria for time-delay fractional systems with a retarded state
    Autorzy:
    Sikora, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/330421.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    fractional dynamical systems
    controllability criteria
    delays in the state
    constraints
    pseudotransition matrix
    Caputo derivative
    układ dynamiczny ułamkowy
    sterowalność
    pochodna ułamkowego rzędu Caputo
    Opis:
    The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative U-controllability are established and proved. Numerical examples illustrate the obtained theoretical results.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2016, 26, 3; 521-531
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Practical Mittag-Leffler stability of quasi-one-sided Lipschitz fractional order systems
    Autorzy:
    Basdouri, Imed
    Kasmi, Souad
    Lerbet, Jean
    Powiązania:
    https://bibliotekanauki.pl/articles/27312007.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    fractional-order systems
    Caputo derivative
    quasi-one-sided Lipschitz condition
    nonlinear systems
    observer design
    output feedback stabilization
    separation principle
    Opis:
    This paper focuses on the global practical Mittag-Leffler feedback stabilization problem for a class of uncertain fractional-order systems. This class of systems is a larger class of nonlinearities than the Lipschitz ones. Based on the quasi-one-sided Lipschitz condition, firstly, we provide sufficient conditions for the practical observer design. Then, we exhibit that practical Mittag-Leffler stability of the closed loop system with a linear, state feedback is attained. Finally, a separation principle is established and we prove that the closed loop system is practical Mittag-Leffler stable.
    Źródło:
    Archives of Control Sciences; 2023, 33, 1; 55--70
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional descriptor continuous-time linear systems described by the Caputo–Fabrizio derivative
    Autorzy:
    Kaczorek, T.
    Borawski, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/330274.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    fractional system
    descriptor system
    continuous time
    linear system
    Caputo–Fabrizio derivative
    układ niecałkowitego rzędu
    układ deskryptorowy
    układ ciągły
    układ liniowy
    Opis:
    The Weierstrass–Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor continuous-time linear systems described by the Caputo–Fabrizio derivative. A method for computing solutions of continuous-time systems is presented. Necessary and sufficient conditions for the positivity and stability of these systems are established. The discussion is illustrated with a numerical example.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2016, 26, 3; 533-541
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and Ulam-Hyers stability of the implicit fractional boundary value problem with ψ-Caputo fractional derivative
    Autorzy:
    Wahash, Hanan A.
    Abdo, Mohammed S
    Panchal, Satish K.
    Powiązania:
    https://bibliotekanauki.pl/articles/122800.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional differential equations
    ψ-fractional integral and derivative
    existence and Ulam-Hyers stability
    fixed point theorem
    równania różniczkowe ułamkowe
    równania różniczkowe cząstkowe
    pochodna ułamkowa
    twierdzenie o punkcie stałym
    pochodna ułamkowa Caputo
    Opis:
    In this paper, we investigate the existence, uniqueness and Ulam-Hyers stability of solutions for nonlinear implicit fractional differential equations with boundary conditions involving a ψ-Caputo fractional derivative. The obtained results for the proposed problem are proved under a new approach and minimal assumptions on the function ƒ . The analysis is based upon the reduction of the problem considered to the equivalent integral equation, while some fixed point theorems of Banach and Schauder and generalized Gronwall inequality are employed to obtain our results for the problem at hand. Finally, the investigation is illustrated by providing a suitable example.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 89-101
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and Ulam-Hyers stability of the implicit fractional boundary value problem with ψ-Caputo fractional derivative
    Autorzy:
    Wahash, Hanan A.
    Abdo, Mohammed S
    Panchal, Satish K.
    Powiązania:
    https://bibliotekanauki.pl/articles/1839794.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional differential equations
    ψ-fractional integral and derivative
    existence and Ulam-Hyers stability
    fixed point theorem
    równania różniczkowe ułamkowe
    równania różniczkowe cząstkowe
    pochodna ułamkowa
    twierdzenie o punkcie stałym
    pochodna ułamkowa Caputo
    Opis:
    In this paper, we investigate the existence, uniqueness and Ulam-Hyers stability of solutions for nonlinear implicit fractional differential equations with boundary conditions involving a ψ-Caputo fractional derivative. The obtained results for the proposed problem are proved under a new approach and minimal assumptions on the function ƒ. The analysis is based upon the reduction of the problem considered to the equivalent integral equation, while some fixed point theorems of Banach and Schauder and generalized Gronwall inequality are employed to obtain our results for the problem at hand. Finally, the investigation is illustrated by providing a suitable example.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 89-101
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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