Analysis of an evolutionary fractional hemivariational inequality with applications

This paper investigates a novel abstract system that includes a fractional differential equation of the Atangana-Baleanu type and a history-dependent evolutionary hemivariational inequality (AB-FDEHI). We demonstrate the unique solvability of this problem by applying a semi-discrete approximation (the so-called Rothe method) and utilizing the surjectivity of a multivalued pseudo-monotone operator theorem. Additionally, we derive a fully discrete approximation of the system (AB-FDEHI), present the error estimates, and demonstrate the convergence result. The results obtained are used to examine a novel frictional contact problem (FCP) involving a viscoelastic material and an obstacle, where the effects of memory terms and wear are taken into account.