Doha, Eid H.Bhrawy, Ali H.Baleanu, DumitruEzz-Eldien, Samer S.2019-12-232019-12-232014Cited References in Web of Science Core Collection: 411687-1847https://doi.org/10.1186/1687-1847-2014-231https://t.ly/xNM2mAccession Number: WOS:000342158400003In this article, an accurate and efficient numerical method is presented for solving the space-fractional order diffusion equation (SFDE). Jacobi polynomials are used to approximate the solution of the equation as a base of the tau spectral method which is based on the Jacobi operational matrices of fractional derivative and integration. The main advantage of this method is based upon reducing the nonlinear partial differential equation into a system of algebraic equations in the expansion coefficient of the solution. In order to test the accuracy and efficiency of our method, the solutions of the examples presented are introduced in the form of tables to make a comparison with those obtained by other methods and with the exact solutions easy.enUniversity of multi-term fractional differential equations; fractional diffusion equations; tau method; shifted Jacobi polynomials; operational matrix; Caputo derivative; HOMOTOPY-PERTURBATION METHOD; FINITE-DIFFERENCE METHODS; NUMERICAL APPROXIMATIONS; INTEGRATIONArticlehttps://doi.org/10.1186/1687-1847-2014-231