Solvability and optimal control of semilinear nonlocal fractional evolution inclusion with Clarke subdifferential

This article deals with a control system governed by a semilinear nonlocal fractional evolution inclusion with Clarke subdifferential and its optimal control. First we establish an existence theorem of the mild solution for the presented control system by applying the measure of noncompactness, a fixed point theorem of a condensing multivalued map and some properties of Clarke subdifferential. Moreover, under some mild conditions, we obtain a result on the existence of an optimal control to the presented control system. Finally, an example is provided to demonstrate the main results.