An efficient Chebyshev-tau method for solving the space fractional diffusion equations

Fractional diffusion equations (FDEs) have recently been paid much attention. Finding accurate and efficient methods for solving FDEs has become an active research undertaking. In this paper, an efficient method based on the shifted Chebyshev-tau idea is presented to solve an initial-boundary value problem for the FDEs. The method is derived by expanding the required approximate solution as the elements of shifted Chebyshev polynomials. Using the operational matrix of the fractional derivative, the problem can be reduced to a set of linear algebraic equations. From a computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous work in the literature and only a small number of shifted Chebyshev polynomials is needed.