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<p>This article studies topological properties of the solution set for a class of Caputo fractional delayed evolution inclusions. Firstly, in the scenario when the cosine family is noncompact, the compactness and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13540_2024_362_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>-property are obtained for the mild solution set. Then, as an application of the above obtained results, the approximative controllability is demonstrated. Finally, an example is given as an illustration.</p>

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Topological properties of the solution set for Caputo fractional evolution inclusions involving delay

  • 期刊论文

  • 发表日期：

    2025年3月4日

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  • Huihui Yang,
  • He Yang

摘要

This article studies topological properties of the solution set for a class of Caputo fractional delayed evolution inclusions. Firstly, in the scenario when the cosine family is noncompact, the compactness and \(R_{\delta }\) R δ -property are obtained for the mild solution set. Then, as an application of the above obtained results, the approximative controllability is demonstrated. Finally, an example is given as an illustration.