A New Class of ψ-Caputo Fractional Viscoelastic Contact Problems with Adhesion in Symmetric Dual Spaces

This paper is dedicated to the discussion of a new long memory ψ-Caputo fractional viscoelastic friction contact problem with adhesion in symmetric dual spaces. In this contact model, the contact condition is described by Clarke-generalized gradient of nonconvex and non-smooth function involving adhesion. Firstly, we investigate a new system involving a ψ-Caputo fractional variational–hemivariational inequalities with history-dependent operators coupled with a nonlinear differential equation. By employing the Rothe method in conjunction with surjectivity results for multivalued pseudomonotone operators, the solvability of weak solutions to ψ-Caputo fractional differential variational–hemivariational inequality system is obtained. Furthermore, we applied the abstract results obtained to the history-dependent viscoelastic contact problem considering adhesion phenomena and provided the existence of solution for this contact problem.