Fractional-order Lagrange polynomials: An application for solving delay fractional optimal control problems

The main purpose of this work is to provide an efficient method for solving delay fractional optimal control problems (DFOCPs). Our method is based on fractional-order Lagrange polynomials (FLPs) and the collocation method. The FLPs are used to achieve a new operational matrix of fractional derivative. Also, we present a delay operational matrix of FLPs. These operational matrices are driven without considering the nodes of Lagrange polynomials. The operational matrices and collocation method are applied to a constrained extremum in order to minimize the performance index. Then, the problem reduces to the solution of a system of algebraic equations. Convergence of the algorithm and approximation of FLPs are proposed. Furthermore, the upper bound of the error for the operational matrix of fractional derivatives is obtained. Numerical tests for demonstrating the efficiency and effectiveness of the method are included. Moreover, the method is used for numerical solution of a mathematical model of chemotherapy in breast cancer.