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

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Abstract

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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  1. Department of Mathematics, Faculty of Science, Benha University, Benha, 13518, Egypt

    A. M. Nagy

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  1. A. M. Nagy
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Nagy, A.M. Non-Standard Finite Difference Schemes for Solving Variable-Order Fractional Differential Equations. Differ Equ Dyn Syst 29, 623–632 (2021). https://doi.org/10.1007/s12591-017-0378-2

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