Numerical study of the two-term time-fractional differential equation using the Lagrange polynomial pseudo-spectral method

Abstract

This paper is about the implementation of the pseudo-spectral method based on the Lagrange polynomials to the numerical study of the multi-term time-fractional differential equations. Also, a semi-discrete approximation scheme used to the conversion of this equation to a system of ordinary fractional differential equations. To maintain the high accuracy of the spectral method, we applied the Mittag-Leffler function for time integration. A comparison of numerical results highlights the accuracy and efficiency of the provided scheme.