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Wyświetlanie 1-15 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:
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:
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:
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:
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:
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:
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
Wyświetlanie 1-15 z 52

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