Matrix approach to discrete fractional calculus II: Partial fractional differential equations [PDF]
Journal of Computational Physics, 2009 33 pages, 12 ...
Igor Podlubny +4 more
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The BEM for numerical solution of partial fractional differential equations
Computers & Mathematics with Applications, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
J. Katsikadelis
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ARA-residual power series method for solving partial fractional differential equations [PDF]
Alexandria Engineering Journal, 2022 In this article a new approach in solving time fractional partial differential equations is introduced, that is, the ARA-residual power series method. The main idea of this technique, depends on applying the ARA-transform and using Taylor's expansion to ...
Aliaa Burqan +3 more
semanticscholar +1 more source
New generalized Mellin transform and applications to partial and fractional differential equations
International Journal of Mathematics and Computer in Engineering, 2023 In this paper, we introduce a generalized Mellin transformation in a general form that encompasses the generalized Mellin transformations found in the literature.
E. Ata, İ. Onur Kıymaz
semanticscholar +1 more source
The solutions of nonlinear fractional partial differential equations by using a novel technique
Open Physics, 2022 In this article, the solutions of higher nonlinear partial differential equations (PDEs) with the Caputo operator are presented. The fractional PDEs are modern tools to model various phenomena more accurately.
Alderremy Aisha Abdullah +6 more
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Fractal and Fractional, 2022 This paper mainly considers the parameter estimation problem for several types of differential equations controlled by linear operators, which may be partial differential, integro-differential and fractional order operators. Under the idea of data-driven
Wenbo Zhang, Wei Gu
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On the Stability of a Hyperbolic Fractional Partial Differential Equation [PDF]
Differential Equations and Dynamical Systems, 2019 In this paper, by means of the Gronwall inequality, the ψ-Riemann-Liouville fractional partial integral and the ψ-Hilfer fractional partial derivative are introduced and some of its particular cases are recovered. Using these results, we investigate the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the solutions of a fractional partial differential ...
J. Vanterler da C. Sousa +1 more
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Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equations [PDF]
Computer Methods in Applied Mechanics and Engineering, 2022 We introduce a sampling based machine learning approach, Monte Carlo physics informed neural networks (MC-PINNs), for solving forward and inverse fractional partial differential equations (FPDEs).
Ling Guo, Hao Wu, Xiao-Jun Yu, Tao Zhou
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Large Fractional Linear Type Differential Equations
International Journal of Analysis and Applications, 2023 This paper aims to handle some types of fractional differential equations with a fractional-order values β>1. In particular, we propose a novel analytical solution called an atomic solution for certain fractional linear type differential equations as ...
Ma'mon Abu Hammad +2 more
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An Implementation Solution for Fractional Partial Differential Equations [PDF]
Mathematical Problems in Engineering, 2013 The link between fractional differentiation and diffusion equation is used in this paper to propose a solution for the implementation of fractional diffusion equations. These equations permit us to take into account species anomalous diffusion at electrochemical interfaces, thus permitting an accurate modeling of batteries, ultracapacitors, and fuel ...
Bertrand, Nicolas +3 more
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