A new class of general fractional differential quasivariational and quasivariational–hemivariational inequalities with variable constraint sets

Abstract

This paper investigates a new general nonlinear system, which comprises a fractional differential equation and a history-dependent quasivariational inequality with a variable constraint set, as well as a quasivariational–hemivariational inequality with a variable constraint set. Such a general nonlinear system can be used to describe a nonlinear quasistatic thermoelastic frictional contact problem of viscoelastic materials with long memory, wear and implicit obstacles. By employing the fixed point theorem of the set-valued mapping, the solvability for such a general nonlinear system is proved under some mild conditions. Moreover, our abstract result is applied to obtain the solvability of a new nonlinear quasistatic thermoelastic frictional contact problem with long memory, wear and implicit obstacles.