Local RBF-FD technique for solving the two-dimensional modified anomalous sub-diffusion equation

The main aim of this paper is to propose an efficient and suitable numerical procedure based on the local meshless collocation method for solving the two-dimensional modified anomalous sub-diffusion equation. The fractional derivative is based on the Riemann-Liouville fractional integral. Firstly, a finite difference scheme with O(τ) has been employed to discrete the time variable and also the local radial basis-finite difference (LRBF-FD) method is used to discrete the spatial direction. For the presented numerical technique, we prove the unconditional stability and also obtain an error bound. We employ a test problem to show the accuracy of the proposed technique. Also, we solve the mentioned model on irregular domain to show the efficincy of the developed technique.