numerical solution of space fractional diffusion equation using shifted gegenbauer polynomials

this paper is concerned with numerical approach for solving space fractional diffusion equation using shifted gegenbauer polynomials, where the fractional derivatives are expressed in caputo sense. the properties of gegenbauer polynomials are exploited to reduce space fractional diffusion equation to a system of ordinary differential equations, that are then solved using finite difference method. some selected numerical simulations of space fractional diffusion equations are presented and the results are compared with the exact solution, also with the results obtained via other methods in the literature. the comparison reveals that the proposed method is reliable, effective and accurate. all the computations were carried out using matlab package.