Application of high-order spectral method for the time fractional mobile/immobile equation

In this paper, a numerical efficient method is proposed for the solution of time fractional mobile/immobile equation. The fractional derivative of equation is described in the Caputo sense. The proposed method is based on a finite difference scheme in time and Legendre spectral method in space. In this approach the time fractional derivative of mentioned equation is approximated by a scheme of order O(τ2−γ) for 0 γ 1. Also, we introduce the Legendre and shifted Legendre polynomials for full discretization. The aim of this paper is to show that the spectral method based on the  egendre polynomial is also suitable for the treatment of the fractional partial differential equations. Numerical examples confirm the high accuracy of proposed scheme.