Numerical Simulation of the Variable Order Fractional Integro-Differential Equation via Chebyshev Polynomials

In this paper, the Chebyshev polynomials method is applied to solve a space-time variable fractional order integro-differential equation. Using operational matrices of Chebyshev polynomials furnished from the Caputo–Prabhakar sense and also suitable collocation points, the variable fractional order integro-differential equation would be converted to the system of algebraic equations. 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. An error bound is proved for the approximate solution obtained by the proposed method. Finally, some numerical examples are presented to demonstrate the accuracy of the proposed method.