Gaussian-radial basis functions for solving fractional parabolic partial integro-differential equations

Abstract

In this investigation, 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 RBF 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. Error analysis of the proposed method is investigated. Numerical examples are provided to show the convenience of the numerical schemes based on the G-RBFs. The results reveal that the method is very efficient and convenient for solving such equations.