A class of Hilfer fractional differential evolution hemivariational inequalities with history-dependent operators

The main purpose of this paper is to study an abstract system which consists of a parabolic hemivariational inequality with a Hilfer fractional evolution equation involving history-dependent operators, which is called a Hilfer fractional differential hemivariational inequality. We first show existence and a priori estimates for the parabolic hemivariational inequality. Then, by using the well-known Bohnenblust-Karlin fixed point theorem, we prove an existence theorem for the Hilfer fractional differential hemivariational inequality.