Optimal control problem governed by a highly nonlinear singular Volterra equation: Existence of solutions and maximum principle

Abstract We consider a Lagrange optimal control problem for a Volterra integral equation of fractional potential type. We prove a theorem on the existence of an optimal solution and derive a maximum principle. The proof of the existence theorem is based on the lower closure theorem for orientor fields due to Cesari and Filippov‐type selection theorem due to Rockafellar. The proof of the maximum principle is based on an extremum principle for smooth problems proved in Idczak and Walczak ( Games . 2020;11:56).