Gene

Quantum mechanics

Banach space

Inequality

Applied mathematics

Biochemistry

Computer science

Constitutive equation

Viscoelasticity

Quasistatic process

Differential operator

Thermodynamics

Physics

Finite element method

Mathematics

Differential (mechanical device)

Transcription factor

Mathematical analysis

Artificial intelligence

Repressor

Chemistry

Operator (biology)

Fractional calculus

Class (philosophy)

Zeitschrift für angewandte Mathematik und Physik

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.

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