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

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