High Order Numerical Scheme for Generalized Fractional Diffusion Equations

被引：0

作者：

Kumar K. ^{[1
]}

Pandey A.K. ^{[2
]}

Pandey R.K. ^{[3
]}

机构：

[1] Department of Sciences (Mathematics), Manav Rachna University, Haryana, Faridabad

[2] School of Business, University of Petrolium and Energy Studies, Uttarakhand, Dehradun

[3] Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Uttar Pradesh, Varanasi

来源：

International Journal of Applied and Computational Mathematics | 2024年 / 10卷 / 3期

关键词：

Caputo fractional derivative; Finite difference scheme; Generalized fractional diffusion equations; Generalized time fractional derivative;

D O I：

10.1007/s40819-024-01725-5

中图分类号：

学科分类号：

摘要：

In this paper, a higher order finite difference scheme is proposed for generalized fractional diffusion equations (GFDEs). The fractional diffusion equation is considered in terms of the generalized fractional derivatives (GFDs) which uses the scale and weight functions in the definition. The GFD reduces to the Riemann–Liouville, Caputo derivatives and other fractional derivatives in a particular case. Due to importance of the scale and the weight functions in describing behaviour of real-life physical systems, we present the solutions of the GFDEs by considering various scale and weight functions. The convergence and stability analysis are also discussed for the finite difference scheme (FDS) to validate the proposed method. We consider test examples for numerical simulation of FDS to justify the proposed numerical method. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2024.

引用

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