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

Yun-Hua Weng,Donal O'Regan,Nan-Jing Huang,Tao Chen

doi:10.15388/namc.2022.27.24649

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.

Highlights

Let Y, Z1, Z2 be three reflexive and separable Banach spaces, and let Z2∗ be the dual space of Z2
We remark that for appropriate and suitable choices of the spaces and the above defined maps, fractional impulsive differential hemivariational inequality (FIDHVI) includes a number of differential variational inequalities as special cases [5, 12, 13, 26, 29]
It is worth mentioning that FIDHVI is a new model, which captures the required characteristics of both the hemivariational inequality and the fractional impulsive differential equation within the same framework

Summary

Introduction

Let Y , Z1, Z2 be three reflexive and separable Banach spaces, and let Z2∗ be the dual space of Z2. FIDHVI can be used to describe the frictional contact problem with the surface traction driven by the fractional impulsive differential equation (see Section 5). Li et al [12] introduced a class of impulsive DVI in finite dimensional spaces and presented some existence and stability results of the solutions under some suitable assumptions. In some practical situations applications, it is necessary to consider FIDHVI

Preliminaries

Existence and uniqueness

A convergence result

An application

Existence and uniqueness for the contact problem

A convergence result for the contact problem