Non-Standard Finite Difference Schemes for Solving Variable-Order Fractional Differential Equations

被引：0
作者：
A. M. Nagy
机构：
[1] Benha University,Department of Mathematics, Faculty of Science
来源：
Differential Equations and Dynamical Systems | 2021年 / 29卷
关键词：
Variable-Order fractional differential equations; Non-standard finite difference schemes; Riemann–Liouville definition; Grünwald–Letinkov definition; viscous-viscoelasticity oscillator model; 34K37; 26A33; 65M06;
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摘要：
A non-standard finite difference (NSFD) methodology of Mickens is a popular method for the solution of differential equations. In this paper, we discusses how we can generalize NSFD schemes for solving variable-order fractional problems. The variable-order fractional derivatives are described in the Riemann–Liouville and Grünwald–Letinkov sense. Special attention is given to the Grünwald–Letinkov definition which is used to approximate the variable-order fractional derivatives. Some applications of the variable-order fractional in viscous-viscoelasticity oscillator model and chaotic financial system are included to demonstrate the validity and applicability of the proposed technique.
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页码：623 / 632
页数：9
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