A numerical study on fractional optimal control problems described by Caputo‐Fabrizio fractional integro‐differential equation

Abstract

AbstractThis paper provides a numerical technique for evaluating the approximate solution of fractional optimal control problems with the Caputo‐Fabrizio (CF) fractional integro‐differential equation. First, due to the Gegenbauer polynomials definition and CF‐fractional derivative, we present the modified operational matrix and complement vector of integration and CF‐fractional derivative. Then, the corresponding discretization of the problem is obtained with the help of the optimization method and the Legendre‐Gauss‐Lobatto (LGL) quadrature rule. The technique of obtaining the proposed matrices and LGL‐quadrature method leads to obtaining the approximate solution with high precision. Moreover, the error of the performance index obtained by the computational method is investigated. Finally, we implement the methodology in several examples. So that, the effect of various parameters defined in the method is illustrated in tables and plots.