On the numerical solutions for the fractional diffusion equation

Fractional differential equations have recently been applied in various area of engineering, science, finance, applied mathematics, bio-engineering and others. However, many researchers remain unaware of this field. In this paper, an efficient numerical method for solving the fractional diffusion equation (F D E) is considered. The fractional derivative is described in the Caputo sense. The method is based upon Chebyshev approximations. The properties of Chebyshev polynomials are utilized to reduce F D E to a system of ordinary differential equations, which solved by the finite difference method. Numerical simulation of F D E is presented and the results are compared with the exact solution and other methods.