History-dependent fractional hemivariational inequality with time-delay system for a class of new frictionless quasistatic contact problems

We study a new frictionless quasistatic contact problem for viscoelastic materials, in which contact conditions are described by the fractional Clarke generalized gradient of nonconvex and nonsmooth functions and a time-delay system. In addition, our constitutive relation is modeled using the fractional Kelvin–Voigt law with long memory. The existence of mild solutions for new history-dependent fractional differential hemivariational inequalities with a time-delay system are obtained by the Rothe method, properties of the Clarke generalized gradient, and a fixed-point theorem.