On a novel modification of the Legendre collocation method for solving fractional diffusion equation

In this paper, a modification of the Legendre collocation method is used for solving the space fractional differential equations. The fractional derivative is considered in the Caputo sense along with the finite difference and Legendre collocation schemes. The numerical results obtained by this method have been compared with other methods. The results show the capability and efficiency of the proposed method.

Keywords:

Fractional diffusion equation , Caputo derivative , Fractional Riccati differential equation , Finite difference , Collocation , Legendre polynomials