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Implicit nonlinear fractional differential equations of variable order [PDF]
Boundary Value Problems, 2021 In this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order.
Amar Benkerrouche +3 more
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Mittag-Leffler Euler ∇-differences for Caputo fractional-order systems
Results in Physics, 2022 Exponential Euler differences have got rapid development recently for integer-order differential equations. But there are few papers focusing on this difference to fractional differential equations.
Tianwei Zhang, Yongkun Li, Jianwen Zhou
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AIMS Mathematics, 2022 We develop four numerical schemes to solve fractional differential equations involving the Caputo fractional derivative with arbitrary kernels. Firstly, we derive the four numerical schemes, namely, explicit product integration rectangular rule (forward ...
Danuruj Songsanga +1 more
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Axioms, 2022 We study a class of nonlinear implicit fractional differential equations subject to nonlocal boundary conditions expressed in terms of nonlinear integro-differential equations.
Djalal Boucenna +2 more
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On the numerical solutions of coupled nonlinear time-fractional reaction-diffusion equations
AIMS Mathematics, 2021 In this paper, we investigate the numerical solutions of coupled nonlinear time-fractional reaction-diffusion equations obtained by applying a procedure that combines the Lie symmetry analysis with the numerical methods.
Alessandra Jannelli +1 more
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Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2021 In this paper, exact and numerical solutions of two dimensional time-fractional diffusion-reaction equation involving the Riemann-Liouville derivative are determined, by applying a procedure that combines the Lie symmetry analysis with the numerical ...
Alessandra Jannelli +1 more
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Fractal and Fractional, 2022 This study is devoted to studying the existence and uniqueness of solutions for Hadamard implicit fractional differential equations with generalized Hadamard fractional integro-differential boundary conditions by utilizing the contraction principle of ...
Limin Guo +3 more
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Existence Results for BVP of a Class of Generalized Fractional-Order Implicit Differential Equations
Communications in Advanced Mathematical Sciences, 2022 In this paper, we study the existence of solutions to boundary value problem for implicit differential equations involving generalized fractional derivative via fixed point methods.
Dvivek Vivek +2 more
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An advanced meshless method for time fractional diffusion equation [PDF]
, 2011 Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are ...
Gu Y. T. +7 more
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Abstract and Applied Analysis, 2021 This article deals with some existence, uniqueness, and Ulam-Hyers-Rassias stability results for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and generalized Hilfer Fractional derivative.
Abdelkrim Salim +3 more
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