The non-standard finite difference method for handling fractional differential systems

Abstract

In this paper, the non-standard finite difference method (in short NSFD) is implemented to give numerical solutions for linear and nonlinear systems of differential equations of fractional order. The Grunwald-Letnikov method is used to approximate the fractional derivative. The proposed algorithm avoids the complexity existed in other numerical approaches. Four linear and nonlinear fractional differential systems including the Lotka-Volterra system are investigated to show the efficiency of NSFD. Numerical results show that the NSFD approach is easy to implement and accurate when applied to differential equations of fractional order.