A system of Hilfer fractional differential equation combined with quasi-hemivariational inequality deriving from contact mechanics

Abstract

The current work is devoted to discussing a new problem that consists of an impulsive fractional differential nonlinear equation in the sense of Hilfer, combined with a quasi-variational and hemivariational inequality. We utilize the fixed point theorem, abstract variational inequalities, and the properties of Hilfer fractional derivatives to ensure that the problem's solution exists and is unique. Furthermore, the findings obtained are used to analyze the existence and uniqueness of the frictional contact problem between an elastic body with impulsive effects on surface traction and a rigid foundation.