Abstract

In this paper, an approximate scheme based on the pseudo-spectral method with the Lagrange polynomial basis on Chebyshev points is proposed to solve the three-dimensional time-fractional diffusion equation. Also, we used the semi-discrete approximation scheme to conversion of this equation to a system of ordinary fractional differential equations. An approach based on the evaluation of the MittagLeffler function is used for the integration along the time variable to preserve the high accuracy of the spectral approximation. An example is performed to illustrate the accuracy and efficiency of the proposed method.