Analysis and simulation of an adhesive contact problem governed by fractional differential hemivariational inequalities with history-dependent operator

Abstract

The main idea of this manuscript is to study an adhesive contact problem with long memory which is governed by a hemivariational inequality and a fractional differential equation. We first prove the existence of a unique solution of the fractional differential hemivariational inequality system. Subsequently, we consider a fully discrete scheme of this system and then focus on deriving error estimates for numerical solutions. To the tail of this manuscript, we present two numerical simulation examples for the adhesive contact problem, which provide numerical evidence to support our theoretical predictions.