A Thermo-Viscoelastic Fractional Contact
Problem with Normal Compliance and
Coulomb’s Friction

Mustapha Bouallala

Cadi Ayyad University, Polydisciplinary faculty, Modeling and Combinatorics Laboratory, Department of Mathematics and Computer Science B.P. 4162, Safi, Morocco
E-mail: bouallalamustaphaan@gmail.com

EL-Hassan Essoufi

Faculty of Science and Technology, Hassan 1st University Settat Laboratory Mathematics, Computer Science and Engineering Sciences (MISI), 26000 Settat, Morocco
E-mail: e.h.essoufi@gmail.com

Received April 29, 2020, revised January 21, 2021.

Abstract

This study concerns the analysis of a quasistatic frictional contact problem between a thermo-viscoelastic body and a thermally conductive foundation. The constitutive relation is built by a fractional Kelvin–Voigt model. The heat conduction is governed by time-fractional of temperature parameter $\theta$. The contact is described by the normal compliance condition and the friction is described by Coulomb’s law. We derive a variational formulation of the problem and prove the existence of a weak solution to the model by using the theory of monotone operator, Caputo derivative, Clark subdifferential, Galerkin method and Banach fixed point theorem.