A study on spectral methods for linear and nonlinear fractional differential equations

Abstract

In this paper, a computational method based on the spectral methods with shifted Jacobi polynomials is applied for the numerical solution of the linear and nonlinear multi-order fractional differential equations. Fractional derivative is described in the Caputo sense. Operational matrix of fractional differential of shifted Jacobi polynomials is stated. This matrix together with the tau method and collocation method are utilised to reduce the linear and nonlinear fractional differential equations to a system of algebraic equations, respectively. The purpose of this paper is to make a comparison between this simple method and other existing methods to show the performance and preciseness of the presented method. Due to this, we used this technique for some illustrative numerical tests which the results demonstrate the validity and efficiency of the method.