Evolution Hemivariational Inequalities Research Articles

Unbounded perturbation of an evolution hemivariational inequality

We consider a perturbed hemivariational inequality. The perturbation is a multivalued mapping the values thereof are not assumed to be convex or bounded. We prove the existence of a solution to our problem and establish a relaxation — approximation result for it through the use of a localized version of Hausdorff-Lipschitzness adapted to the unbounded case.

A class of time-optimal feedback control for fractional neutral evolution hemivariational inequalities with fixed delay

ABSTRACT In this paper, we study a class of optimal feedback control for a neutral fractional system with hemivariational inequalities. Initially, we derive some existence results of mild solutions for the system by applying the Marteli's fixed point theorem of multivalued maps, properties of generalized Clarke's subdifferential and semigroup operators. Then, by using the Filippov theorem and the Cesari property, a new set of sufficient conditions are formulated to ensure the existence results of a feasible pair for the feedback control systems. Also, we apply our main results to obtain the optimal feedback control pair. Further, we investigate the time-optimal feedback control for our control system. In the end, an example is given to illustrate our theory.

Feedback control problems for a class of backward Riemann-Liouville fractional evolution hemivariational inequalities with dual operators

Feedback control problems for a class of backward Riemann-Liouville fractional evolution hemivariational inequalities with dual operators

Control systems described by a class of Riemann-Liouville fractional semilinear evolution hemivariational inequalities

Control systems described by a class of Riemann-Liouville fractional semilinear evolution hemivariational inequalities

A class of Hilfer fractional differential evolution hemivariational inequalities with history-dependent operators

A class of Hilfer fractional differential evolution hemivariational inequalities with history-dependent operators

An Investigation on Existence and Optimal Feedback Control for Fractional Neutral Stochastic Evolution Hemivariational Inequalities

An Investigation on Existence and Optimal Feedback Control for Fractional Neutral Stochastic Evolution Hemivariational Inequalities

Differential Evolution Hemivariational Inequalities with Anti-periodic Conditions

Differential Evolution Hemivariational Inequalities with Anti-periodic Conditions

Hilfer fractional neutral stochastic Sobolev-type evolution hemivariational inequality: Existence and controllability☆

This paper discusses the approximate controllability of hemivariational inequalities of the Sobolev-type Hilfer fractional neutral stochastic evolution system. Firstly, by using fixed point theorems, fractional calculus, Hilfer fractional derivatives, multivalued maps and stochastic analysis, for stochastic fractional evolution systems, we demonstrate mild solutions. Whereupon we introduce necessary conditions that ensure the approximate controllability of stochastic fractional systems. As a final step, we define our primary outcomes using an example.

Hilfer fractional neutral stochastic integro‐differential evolution hemivariational inequalities and optimal controls

The focus of this study is a control system with a nonlocal state that is driven by a neutral stochastic integro‐differential evolution hemivariational inequality known as Hilfer fractional (HF). In order to demonstrate effective requirements for the existence of mild solutions to the relevant control system, we first make use of the features of the extended Clarke subdifferential and a fixed point theorem for multivalued functions. We next prove that there are optimal state‐control sets that are induced by HF neutral stochastic integro‐differential evolution hemivariational inequalities with a nonlocal condition by using limited Lagrange optimal structures. The distinctiveness of the control system's solutions is not taken into consideration while developing optimal control outcomes. At last, an example is employed to go over the major findings.

Existence of Sobolev-Type Hilfer Fractional Neutral Stochastic Evolution Hemivariational Inequalities and Optimal Controls

This article concentrates on a control system with a nonlocal condition that is driven by neutral stochastic evolution hemivariational inequalities (HVIs) of Sobolev-type Hilfer fractional (HF). In order to illustrate the necessary requirements for the existence of mild solutions to the required control system, we first use the characteristics of the modified Clarke sub-differential and a fixed point approach for multivalued functions. Then, we show that there are optimal state-control sets that are driven by Sobolev-type HF neutral stochastic evolution HVIs utilizing constrained Lagrange optimal systems. The optimal control (OC) results are created without taking the uniqueness of the control system solutions into account. Finally, the main finding is shown by an example.

Optimal Control Problems for Hilfer Fractional Neutral Stochastic Evolution Hemivariational Inequalities

In this paper, we concentrate on a control system with a non-local condition that is governed by a Hilfer fractional neutral stochastic evolution hemivariational inequality (HFNSEHVI). By using concepts of the generalized Clarke sub-differential and a fixed point theorem for multivalued maps, we first demonstrate adequate requirements for the existence of mild solutions to the concerned control system. Then, using limited Lagrange optimal systems, we demonstrate the existence of optimal state-control pairs that are regulated by an HFNSEHVI with a non-local condition. In order to demonstrate the existence of fixed points, the symmetric structure of the spaces and operators that we create is essential. Without considering the uniqueness of the control system’s solutions, the best control results are established. Lastly, an illustration is used to demonstrate the major result.

Topological properties of solution sets for nonlinear evolution hemivariational inequalities and applications

The purpose of this paper is to investigate the topological properties of solution sets for a class of nonlinear evolution hemivariational inequalities. We firstly obtain the nonemptiness and the compactness of the solution set for hemivariational inequalities by applying the Kakutani–KyFan fixed point theorem, Gronwall’s inequality and the multivalued analysis. Then by using Hyman’s theorem, we show that the solution set for presented problem is an Rδ set. Finally, some applications to infinite dimensional control systems are given.

Approximation and convergence analysis of optimal control for non-instantaneous impulsive fractional evolution hemivariational inequalities

In this work, a fractional evolution hemivariational inequalities driven by non-instantaneous impulses is studied. The solvability of the proposed system is obtained by fractional calculus, properties of generalized Clarke’s subdifferential and Dhage fixed point theorem. This article also presents the construction of the lower-dimensional approximation system for the proposed model, and its convergence of the mild solution is obtained. Besides, by considering suitable assumptions, the local approximation and uniform convergence results are established for the proposed system’s mild solution. Furthermore, sufficient conditions for the existence of Lagrange optimal control problem and convergence analysis of optimal control for the proposed model are formulated and proved. At last, an example is given for the illustration of invented new theoretical results.

New discussion regarding approximate controllability for Sobolev-type fractional stochastic hemivariational inequalities of order [formula omitted

In this paper, we deal with the approximate controllability of Sobolev-type fractional stochastic evolution hemivariational inequalities of order r∈(1,2). Firstly, by using stochastic analysis, fractional calculus, sine and cosine family operators, and fixed point theorems of multivalued maps, we show the existence of mild solutions for the fractional stochastic evolution systems. Then we provide a sufficient condition to guarantee the approximate controllability of the stochastic evolution systems. Next, our results cover problems involving nonlocal conditions. Finally, we present theoretical and practical applications to support the validity of the study.

An Analysis Regarding to Approximate Controllability for Hilfer Fractional Neutral Evolution Hemivariational Inequality

An Analysis Regarding to Approximate Controllability for Hilfer Fractional Neutral Evolution Hemivariational Inequality

On approximate controllability for systems of fractional evolution hemivariational inequalities with Riemann-Liouville fractional derivatives

On approximate controllability for systems of fractional evolution hemivariational inequalities with Riemann-Liouville fractional derivatives

Optimal control of an evolution hemivariational inequality involving history-dependent operators

In this paper we consider a class of feedback control systems described by an evolution hemivariational inequality involving history-dependent operators. Under the mild conditions, first, we prove a priori estimates of the solutions to the feedback control system. Then, an existence theorem for the feedback control system is obtained by using the well-known Bohnenblust-Karlin fixed point theorem. Moreover, we consider an optimal control problem driven by the feedback control system, and establish its solvability. Finally, a parabolic partial differential system with Clarke subgradient term is considered to illustrate the applicability of the theoretical results.

Approximate controllability of non-autonomous second-order evolution hemivariational inequalities with nonlocal conditions

The goal of this paper is to deal with approximate controllability of control systems described by non-autonomous second-order evolution hemivariational inequalities with nonlocal conditions in Hilbert spaces. First we define the concept of mild solution relying on the existence of an evolution operator for the corresponding linear equation and the property of Clarke subdifferential. Next, the solvability and approximate controllability are considered by means of a fixed-point strategy. Finally, two examples are provided to illustrate our main results.

Control systems described by a class of fractional semilinear evolution hemivariational inequalities and their relaxation property

ABSTRACT We are concerned with control systems described by a class of semilinear fractional evolution hemivariational inequalities in separable reflexive Banach spaces. The constraint on the control is a nonconvex valued multivalued function which is lower semicontinuous with respect to the variable states. Along with the original system we also consider the system in which the constraint on the control is the upper semicontinuous convex valued regularization of the original constraint. We obtain the existence results of the control systems and the relaxation property among the solution sets of these systems. In the end, an example is provided to illustrate the application of the obtained theory.

Results on approximate controllability of Sobolev type fractional stochastic evolution hemivariational inequalities

AbstractIn our article, we primarily concentrate on the approximate controllability results for Sobolev type fractional stochastic evolution hemivariational inequalities. By applying the facts related to fractional calculus, and fixed‐point technique, the principal results are proved. Initially, we are concentrating the existence and continue to prove the controllability of the fractional evolution system. In the end, we present an example to demonstrate the theory.