This paper presents, a novel semi-analytical algorithm, based on the Chebyshev collocation method, for the solution of space-fractional diffusion equations. The original fractional equation is transformed into a system of ordinary differential equations (ODEs) by the Chebyshev collocation method. A new semi-analytical method is then used to approximate the solution of the resulting system. To emphasize the reliability of the new scheme, a convergence analysis is presented. It is shown that highly accurate solutions can be achieved with relatively few approximating terms and absolute errors are rapidly decrease as the number of approximating terms is increased. By presenting some numerical examples, we show that the proposed method is a powerful and reliable algorithm for solving space-fractional diffusion equations and can be extended to solve another space-fractional partial differential equations. Comparison with other methods in the literature, demonstrates that the proposed method is both efficient and accurate.
