A numerical scheme for solving variable order Caputo-Prabhakar fractional integro-differential equation

Document Type : Research Paper

Authors

1 Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran

2 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

Abstract

In this paper we apply the Chebyshev polynomials method for the numerical solution of a class of variable-order fractional integro-differential equations with initial conditions. Moreover, a class of variable-order fractional integro-differential equations with fractional derivative of Caputo-Prabhakar sense is considered. The main aim of the Chebyshev polynomials method is to derive four kinds of operational matrices of Chebyshev polynomials. With such operational matrices, an equation is transformed into the products of several dependent matrices, which can also be viewed as the system of linear equations after dispersing the variables. Finally, numerical examples have been presented to demonstrate the accuracy of the proposed method, and the results have  been compared with the exact solution.

Keywords