Time-fractional effects in a frictionless contact problem with a history-dependent operator

In this paper, we investigate a novel model problem involving a viscoelastic, frictionless contact model characterized by history-dependent operators. The constitutive relation is formulated based on a time-fractional Kelvin–Voigt model. We represent the contact by incorporating normal compliance within the framework of a time-fractional derivative. In addressing the contact problem, we begin by formulating its weakness and subsequently verify the existence of a solution within this framework. Finally, we study the solution’s behavior concerning the integral term and its relation to the solution, while also presenting convergence results.