Chebyshev collocation scheme and Finite difference method plays central roles for solving fractional differential equations (FDE). Therefore purpose of this paper is to solve fractional mathematical problem of diffusion by Chebyshev collocation method which turns the original problems into the system of fractional ordinary differential and algebraic equations by imposing orthogonality property. This system is solved by implementing Finite difference method. The numerical illustrations confirm that the combination of these two methods allow us to establish one of the best truncated solution in the series form.