Combination of Sinc and radial basis functions for time-space fractional diffusion equations

We study the combination of the Sinc and the Gaussian radial basis functions (GRBF) to develop the numerical methods for the time--space fractional diffusion equations with the Riesz fractional derivative. The GRBF is used to approximate the unknown function in spatial direction and the Sinc quadrature rule associated with double exponential transformation is applied to approximate the arising integrals.  Three practical examples are considered for testing the ability of the proposed method.

Keywords:

Fractional diffusion equations , Sinc method , double exponential transformation , Gaussian radial basis functions