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, FPPI-DEs 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. [ABSTRACT FROM AUTHOR]