Solution of two-dimensional modified anomalous fractional sub-diffusion equation via radial basis functions (RBF) meshless method

This paper is devoted to the radial basis functions (RBFs) meshless approach for the solution of two-dimensional modified anomalous fractional sub-diffusion equation. The fractional derivative of equation is described in the Riemann-Liouville sense. In this method we discretize the time fractional derivatives of mentioned equation by integrating both sides of it, then we will use the Kansa approach to approximate the spatial derivatives. We prove the stability and convergence of time-discretized scheme using energy method. The main aim of this paper is to show that the meshless method based on the radial basis functions and collocation approach is also suitable for the treatment of the fractional partial differential equations. Numerical results obtained from solving this problem on the rectangular, circular and triangular domains demonstrate the theoretical results and efficiency of the proposed scheme.