Solving a Class of Fractional Optimal Control Problems by Homotopy Analysis Method

In this paper, an analytical approximate solution is introduced for a class of fractional optimal control problems. The proposed method utilizes the homotopy analysis method (HAM) to solve the extreme conditions obtained from the Pontryagin's maximum principle. Due to its high computing demands, HAM cannot solve this kind of problem for more than two iterations. We propose lemma from Rudin to overcome this problem. Next, the convergence of the method is illustrated, and the fractional derivative in the dynamical systems is considered in the Caputo sense. Finally, three examples are given to demonstrate the simplicity and efficiency of the proposed method.