a numerical scheme for solving variable order caputo-prabhakar fractional integro-differential equation

In this paper, we apply the chebyshev polynomials for the numerical solution of variable-order fractional integro–differential equations with initial conditions. moreover, a class of variable-order fractional integro–differential equations with a fractional derivative of caputo–prabhakar sense is considered. the main aim of the chebyshev polynomials is to derive four kinds of operational matrices of these 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.