A meshless local radial point interpolation method for solving two-dimensional time fractional advection-diffusion equation

In the current work, an efficient numerical method is proposed to study the two dimensional time fractional advection-diffusion equation (TFADE) with Caputo fractional derivative of order $\alpha (0 \alpha\leq 1)$. For this purpose a meshless local weak formulation is considered for the interior points while the Dirichlet boundary is imposed directly. In this method, radial point interpolation basis functions are used as the shape functions. Finally, a numerical example is presented to verify the efficiency, validity and accuracy of the method