Coupled time-fractional hemivariational inequalities in frictional thermo-viscoelastic contact problem

This study examines a quasistatic frictional contact problem involving a thermo-viscoelastic body interacting with a thermally conductive foundation. The constitutive behavior is described by a fractional Kelvin–Voigt model utilizing the Caputo derivative. Heat conduction is modeled through time-fractional displacement and temperature parameters. The contact, friction, and heat exchange are governed by Clarke's subdifferential boundary conditions. The problem is weakly formulated as a system of two coupled time-fractional hemivariational inequalities. The existence of solutions is established by reducing the system to a single time-fractional hemivariational inequality, leveraging recent advances in the theory of time-fractional hemivariational inequalities.