A class of fractional differential hemivariational inequalities with application to contact problem

By Shengda Zeng, Zhenhai Liu, Stanislaw Migórski. 2018

145 citations recorded by the source corpus.

In this paper, we study a class of generalized differential hemivariational inequalities of parabolic type involving the time fractional order derivative operator in Banach spaces. We use the Rothe method combined with surjectivity of multivalued pseudomonotone operators and properties of the Clarke generalized gradient to establish existence of solution to the abstract inequality. As an illustrative application, a frictional quasistatic contact problem for viscoelastic materials with adhesion is investigated, in which the friction and contact conditions are described by the Clarke generalized gradient of nonconvex and nonsmooth functionals, and the constitutive relation is modeled by the fractional Kelvin–Voigt law.

Subfields: Automotive Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/d2b9191dcf57947dc32da8de488c7171d3d15d98