A new class of fractional impulsive differential hemivariational inequalities with an application

TL;DR

This paper introduces a novel class of fractional impulsive differential hemivariational inequalities, establishing existence, uniqueness, and stability results, and applies these to a frictional contact problem with surface traction.

Contribution

The paper develops a new framework combining hemivariational inequalities with fractional impulsive differential equations, providing existence, uniqueness, and stability results.

Findings

Proved existence and uniqueness of solutions.

Established stability under perturbations.

Applied results to a frictional contact problem.

Abstract

We consider a new fractional impulsive differential hemivariational inequality which captures the required characteristics of both the hemivariational inequality and the fractional impulsive differential equation within the same framework. By utilizing a surjectivity theorem and a fixed point theorem, we establish an existence and uniqueness theorem for such a problem. Moreover, we investigate the perturbation problem of the fractional impulsive differential hemivariational inequality to prove a convergence result which describes the stability of the solution in relation to perturbation data. Finally, our main results are applied to obtain some new results for a frictional contact problem with the surface traction driven by the fractional impulsive differential equation.