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

被引：2
作者：
Nagy, A. M. [1 ]
机构：
[1] Benha Univ, Dept Math, Fac Sci, Banha 13518, Egypt
来源：
DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS | 2021年 / 29卷 / 03期
关键词：
Variable-Order fractional differential equations; Non-standard finite difference schemes; Riemann-Liouville definition; Grunwald-Letinkov definition; viscous-viscoelasticity oscillator model; SHIFTED CHEBYSHEV POLYNOMIALS; CALCULUS; DYNAMICS; KIND;
D O I：
10.1007/s12591-017-0378-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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 Grunwald-Letinkov sense. Special attention is given to the Grunwald-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.
引用
收藏
页码：623 / 632
页数：10
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