On the fractional optimal control problems with a general derivative operator

Abstract

This paper deals with a general form of fractional optimal control problems involving the fractional derivative with singular or non-singular kernel. The necessary conditions for the optimality of these problems are derived and a new numerical method is designed to solve these equations effectively. Simulation results indicate that the proposed method works well and provides satisfactory results with regard to accuracy and computational effort. Comparative results also verify that a particular case with Mittag-Leffler kernel improves the performance of the controlled system in terms of the transient response compared to the other fractional- and integer-order derivatives.