On the Fractional Optimal Control Problems with Singular and Non–Singular Derivative Operators: A Mathematical Derive

The aim of this paper is to design an efficient numerical method to solve a class of time fractional optimal control problems. In this problem formulation, the fractional derivative operator is consid- ered in three cases with both singular and non–singular kernels. The necessary conditions are derived for the optimality of these problems and the proposed method is evaluated for different choices of derivative operators. Simulation results indicate that the suggested technique works well and pro- vides satisfactory results with considerably less computational time than the other existing methods. Comparative results also verify that the fractional operator with Mittag–Leffler kernel in the Caputo sense improves the performance of the controlled system in terms of the transient response compared to the other fractional and integer derivative operators.