Fractional Reduced Differential Transform Method for Solving Mutualism Model with Fractional Diffusion

Abstract

This study presents the fractional reduced differential transform method for a nonlinear mutualism model with fractional diffusion. The fractional derivatives are described by Caputo's fractional operator. In this method, the solution is considered as the sum of an infinite series. Which converges rapidly to the exact solution. The method eliminates the need to use Adomian's polynomials to calculate the nonlinear terms. To show the efficiency and accuracy of this method, we compared the results of the fractional derivatives orders with the ordinary derivative order index α=1 for the nonlinear mutualism model with fractional diffusion. Approximate solutions for different values of the fractional derivatives together with non-fractional derivatives and absolute errors are represented graphically in two and three dimensions. From all numerical results, we can conclude the efficiency of the proposed method for solving different types of nonlinear fractional systems of partial differential equations over existing methods.