Existence And Approximate Controllability for a class of Fractional Order Hemivariational Inequalities

TL;DR

This paper investigates the existence and approximate controllability of fractional differential control problems governed by nonlinear hemivariational inequalities in Hilbert spaces, providing theoretical results and an illustrative example.

Contribution

It establishes the existence of solutions and sufficient conditions for approximate controllability of fractional hemivariational inequalities, extending controllability theory to nonlinear fractional systems.

Findings

Existence of mild solutions for fractional control inclusion problems.

Sufficient conditions for approximate controllability are derived.

Results are validated through a practical example.

Abstract

This paper discusses the approximate controllability of a fractional differential control problem driven by a nonlinear hemivariational inequality in a Hilbert space. First, we prove the existence of a mild solution for a fractional control inclusion problem which is equivalent to a hemivariational inequality by using the nonsmooth analysis and fixed point technique. Further, we established sufficient conditions for the approximate controllability of our inclusion problem by taking corresponding linear system is approximately controllable. The existence and controllability results obtained for the inclusion problem are valid for considered nonlinear hemivariational problem. Finally, we provide an example to illustrate the efficiency of the developed results.