Fractional Optimal Control Problems in the Sense of ψ ‐Caputo Fractional Derivative

ABSTRACT We discuss, in this article, two major topics. First, we address the study and investigation of a generalized fractional optimal control problem (FOCP) involving a fractional derivative defined with respect to another function. We consider a cost functional, to be minimized, and explore an optimal control solution together with its corresponding trajectory. For this aim, we derive the necessary optimality conditions for the considered problem, from which we deduce the expression of optimal control. Second, we provide a numerical scheme allowing us to solve the equations derived from the optimality conditions. Further, we compare the obtained numerical results with already existing ones so that we can show the efficiency of our proposed approach in comparison with the others previously available in the literature.