CONSTRUCTION OF NON-STANDARD FINITE DIFFERENCE METHOD FOR SOLVING JUMARIE TYPE FRACTIONAL DIFFERENTIAL MODEL USING MICKENS SCHEME

Abstract

In this paper we construct Non-standard finite difference scheme (NSFDS) forthe Jumarie type fractional differential system in-terms of Mittag-Leffler function by using Mickens scheme given in the literature by Roegers. After developing this method, the algorithmis applied in physical system of fractional differential equations. The analytical results obtained are then compared with the numerical solutions by using error graphs and heatmap graphs. The efficiency of the scheme is established as it aligns with the exact solution precisely. We also use convergence maps for the NSFDS by showing faster convergence aswe decrease the step size.