History-dependent fractional hemivariational inequality with time-delay system for a class of new frictionless quasistatic contact problems

We study a new frictionless quasistatic contact problem for viscoelastic materials, in which contact conditions are described by the fractional Clarke generalized gradient of nonconvex and nonsmooth functions and a time-delay system. In addition, our constitutive relation is modeled using the fractional Kelvin–Voigt law with long memory. The existence of mild solutions for new history-dependent fractional differential hemivariational inequalities with a time-delay system are obtained by the Rothe method, properties of the Clarke generalized gradient, and a fixed-point theorem.

Gap Functions and Error Bounds for Variational–Hemivariational Inequalities

In this paper we investigate the gap functions and regularized gap functions for a class of variational–hemivariational inequalities of elliptic type. First, based on regularized gap functions introduced by Yamashita and Fukushima, we establish some regularized gap functions for the variational–hemivariational inequalities. Then, the global error bounds for such inequalities in terms of regularized gap functions are derived by using the properties of the Clarke generalized gradient. Finally, an application to a stationary nonsmooth semipermeability problem is given to illustrate our main results.

On nonsmooth multiobjective fractional programming problems involving (p, r)− ρ −(η ,θ)- invex functions

A class of multiobjective fractional programming problems (MFP) is considered where the involved functions are locally Lipschitz. In order to deduce our main results, we introduce the definition of (p,r)?? ?(?,?)-invex class about the Clarke generalized gradient. Under the above invexity assumption, sufficient conditions for optimality are given. Finally, three types of dual problems corresponding to (MFP) are formulated, and appropriate dual theorems are proved.