Gaussian-Radial Basis Functions for Solving Fractional Parabolic Partial Integro-Differential Equations

In this paper, we solve the Caputo's fractional parabolic partial integro-differential equations (FPPI-DEs) by Gaussian-radial basis functions (G-RBFs) method. The main idea for solving these equations is based on the radial basis functions (RBFs) which also provides approaches to higher dimensional spaces. In the suggested method, FPPIDEs are reduced to nonlinear algebraic systems. We propose to apply the collocation scheme using G-RBFs to approximate the solutions of FPPI-DEs. Numerical examples are provided to show the convenience of the numerical scheme based on the G-RBFs. The results reveal that the presented method is very efficient and convenient for solving such problems.