A high-order scheme for time-space fractional diffusion equations with Caputo-Riesz derivatives

Sayyar, Golsa; Hosseini, Seyed Mohammad; Mostajeran, F.

doi:10.1016/j.camwa.2021.11.002

Computers & Mathematics with Applications

2021

DOI: 10.1016/j.camwa.2021.11.002

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A high-order scheme for time-space fractional diffusion equations with Caputo-Riesz derivatives

Golsa Sayyar

Seyed Mohammad Hosseini

F. Mostajeran

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Cited by 5 publications

References 28 publications

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Solving Multi‐Term Time‐Fractional Diffusion Equations Using a High‐Order Fractional Finite Difference Scheme Accompanied by Neural Network Techniques

Mostajeran,

Hosseini

2024

Numerical Methods Partial

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This article is devoted to solving multi‐term time‐fractional diffusion equations with a high‐order finite difference scheme. We approximate the temporal fractional derivatives by the L1‐2‐3 formula, an expansion of the L1 formula with higher accuracy. We employ neural network strategies and automatic differentiation techniques for approximating integer‐order derivatives. In the present work, we propose very important lemmas and theorems to prove the unconditional stability and convergence of the proposed scheme. Extensive numerical experiments for one‐ and two‐dimensional problems, especially for curved boundaries, confirm the theoretical convergence orders. Comparisons with fractional physics‐informed neural networks and finite difference methods in solving the multi‐term time‐fractional diffusion equations demonstrate the superiority of the proposed method. It is also illustrated that the proposed scheme can efficiently and accurately extract the pattern of the solutions even when noise corruption up to ten percent is imposed on the forcing term.

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Solving Multi‐Term Time‐Fractional Diffusion Equations Using a High‐Order Fractional Finite Difference Scheme Accompanied by Neural Network Techniques

Mostajeran,

Hosseini

2024

Numerical Methods Partial

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Bicomplex Caputo Derivative: A Comparative Study with Bicomplex Riemann–Liouville Operators and Applications

Goswami,

Kumar

2024

Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci.

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Fractional models of falling object with linear and quadratic frictional forces considering Caputo derivative

Türkyılmazoğlu¹,

Altanji²

2023

Chaos, Solitons & Fractals

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A high-order scheme for time-space fractional diffusion equations with Caputo-Riesz derivatives

Cited by 5 publications

References 28 publications

Solving Multi‐Term Time‐Fractional Diffusion Equations Using a High‐Order Fractional Finite Difference Scheme Accompanied by Neural Network Techniques

Solving Multi‐Term Time‐Fractional Diffusion Equations Using a High‐Order Fractional Finite Difference Scheme Accompanied by Neural Network Techniques

Bicomplex Caputo Derivative: A Comparative Study with Bicomplex Riemann–Liouville Operators and Applications

Fractional models of falling object with linear and quadratic frictional forces considering Caputo derivative

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