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<p>In this article, our focus is on exploring the topological characteristics of the corresponding mild solution set for the control problem driven by fractional delay differential quasi-hemivariational inequalities. The proof is based on arguments of the theory of fractional calculus, measure of noncompactness, some characteristics of Clarke subdifferential and some fixed point theories. First, we show that the mild solution set is a nonempty, compact and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13540_2025_432_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(R_{\delta }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mi>δ</mi> </msub> </math></EquationSource> </InlineEquation>-set. Moreover, we demonstrate that the reachability set of the associated control problem remains invariant under nonlinear perturbations. Then a result on the existence of the related optimal control and a approximate controllability result of the corresponding control problem are derived. Finally, a concrete example is provided clarify abstract results.</p>

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Topological properties of solution sets for control problems driven by fractional delay differential quasi-hemivariational inequalities and applications

  • 期刊论文

  • 发表日期：

    2025年7月28日

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  • Yirong Jiang,
  • Xiaoling Qin,
  • Guoji Tang

摘要

In this article, our focus is on exploring the topological characteristics of the corresponding mild solution set for the control problem driven by fractional delay differential quasi-hemivariational inequalities. The proof is based on arguments of the theory of fractional calculus, measure of noncompactness, some characteristics of Clarke subdifferential and some fixed point theories. First, we show that the mild solution set is a nonempty, compact and \(R_{\delta }\) R δ -set. Moreover, we demonstrate that the reachability set of the associated control problem remains invariant under nonlinear perturbations. Then a result on the existence of the related optimal control and a approximate controllability result of the corresponding control problem are derived. Finally, a concrete example is provided clarify abstract results.