Solution of space-time fractional diffusion equation involving fractional Laplacian with a local radial basis function approximation

Radial basis function-based finite difference (RBF-FD) schemes generalize finite difference methods, providing flexibility in node distribution as well as the shape of the domain. In this paper, we consider a numerical formulation based on RBF-FD for solving a time-space fractional diffusion problem defined using a fractional Laplacian operator. The model problem is simplified into a local problem in space using the Caffarelli-Silvestre extension method. The space derivatives in the resulting problem are then discretized using a local RBF-based finite difference method, while L1 approximation is used for the fractional time derivative. Results obtained using the proposed scheme are then compared with that given in the existing literature.