Hilfer fractional evolution hemivariational inequalities with nonlocal initial conditions and optimal controls

Abstract

In this paper, we mainly consider a control system governed by a Hilfer fractional evolution hemivariational inequality with a nonlocal initial condition. We first establish sufficient conditions for the existence of mild solutions to the addressed control system via properties of generalized Clarke subdifferential and a fixed point theorem for condensing multivalued maps. Then we present the existence of optimal state-control pairs of the limited Lagrange optimal systems governed by a Hilfer fractional evolution hemivariational inequality with a nonlocal initial condition. The optimal control results are derived without uniqueness of solutions for the control system.

Keywords

• Hilfer fractional evolution equation
• optimal state-control pairs
• hemivariational inequalities
• nonlocal initial condition