A collocation method for fractional diffusion equation in a long time with Chebyshev functions

In this paper, our aim is to find a new numerical method for diffusion equation with fractional derivative on time and space. The employed fractional derivative is in the Caputo sense. Also, by employing a class of shifted Chebyshev polynomials for the space area and a collection of rational Chebyshev functions for the time domain and then using collocation method, we obtain an algebraic system of equations. The convergence estimate of the new scheme have been concluded. Finally, we evaluate results of this method with other numerical methods.