Weak solvability of a fractional viscoelastic frictionless contact problem

The goal of this paper is to study a quasistatic frictionless contact problem for a viscoelastic body in which the constitutive equation is modeled with the fractional Kelvin-Voigt law and the contact condition is described by the Clarke subdifferential of a nonconvex and nonsmooth functional. The variational formulation of this problem is provided in the form of a fractional hemivariational inequality. In order to solve this inequality, we apply the Rothe method and prove that the associated abstract Volterra inclusion has at least one solution.