A New Numerical Approach for Solving Fractional Optimal Control Problems with the Caputo–Fabrizio Fractional Operator

Abstract

In this study, the necessary optimality conditions are achieved for a class of fractional optimal control problems (FOCPs) involving the Caputo–Fabrizio (CF) fractional derivative. We offer a new numerical method based on the Chebyshev cardinal functions for solving the problem. Our goal was to reduce the original problem into a nonlinear system of algebraic equations. For doing this, we approximate the state and control variables in terms of the Chebyshev cardinal functions. The operational matrices (OMs) of left and right CF fractional integrals are also derived for the Chebyshev cardinal functions. Error estimation and convergence analysis of the method are also introduced. The numerical results illustrate the effectiveness and the rapid convergence of the proposed technique. Due to the high accuracy of the solutions, the suggested method is very useful for numerical techniques in control theory.