Fractional-Order Chelyshkov Collocation Method for Solving Systems of Fractional Differential Equations

Abstract

This paper presents an efficient method for solving systems of fractional differential equations by using the fractional-order Chelyshkov functions (FCHFs). The fractional derivative and the fractional integral are considered in the Caputo sense and the Riemann–Liouville sense, respectively. The proposed method is based on using the operational matrix of fractional integration for FCHFs, together with the spectral collocation method to transform the system of fractional differential equations into a system of algebraic equations. The convergence of the presented method is demonstrated. The performance of the presented method is tested through various examples of systems of fractional differential equations. A comparison with some existing methods shows that the presented method can be successfully used to solve systems of fractional differential equations with accuracy and efficiency.