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 fractionalmobile/immobile equation. the fractional derivative of equation is described in the caputosense. the proposed method is based on a finite difference scheme in time and legendrespectral method in space. in this approach the time fractional derivative of mentioned equationis approximated by a scheme of order o(τ2−γ) for 0 < γ < 1. also, we introduce the legendreand shifted legendre polynomials for full discretization. the aim of this paper is to show thatthe spectral method based on the legendre polynomial is also suitable for the treatment ofthe fractional partial differential equations. numerical examples confirm the high accuracy ofproposed scheme.