Numerical solution of fractional diffusion equation by Chebyshev collocation method and residual power series method

In this paper, we propose an efficient Chebyshev collocation scheme to solve diffusion problem including time fractional diffusion equation considering the fractional derivative in the Liouville-Caputo sense. By making use of shifted Chebyshev polynomial series and their orthogonality properties, the problem is reduced to the system of fractional ordinary differential equations which can be solved by residual power series method (RPSM) with the help of the given scheme and boundary conditions. The numerical examples shows that the method is reliable and effective to construct the numerical solution of fractional diffusion equation. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Fai Lilly of Engineering, Alexandria University.