Pontryagin’s maximum principle for a fractional integro-differential Lagrange problem

In this paper, we study an optimal control problem of Lagrange type in which a control system is described by a nonlinear and singular integro-differential equation of Volterra type with a Caputo derivative. The necessary first-order optimality conditions for a local in (y,u,v) solution (in the form of a maximum principle) for the considered problem are derived. Our approach to deriving these conditions is based on an extremum principle for an abstract optimal control problem obtained in Idczak and Walczak (2020), where the main assumption is smoothness in (y,u,v) of a cost and an operator describing constraints. •Proof and applying of the Maximum Principle (PMP) for the FOCP under consideration.