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<p>In this article, we explore a category of semilinear perturb evolution inclusions that incorporate a nonlocal condition, specifically involving the Hilfer fractional derivative characterized by an order <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7913_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">\(0&lt; \epsilon &lt; 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>&lt;</mo> <mi>ϵ</mi> <mo>&lt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and type <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7913_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="72" /> </InlineMediaObject> <EquationSource Format="TEX">\(0 \le \rho \le 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>≤</mo> <mi>ρ</mi> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Our approach focuses on proving the existence and exact controllability of solutions by applying well-established concepts in fractional calculus, set-valued mappings, and a hybrid fixed point theorem tailored for two operators. We find a different approach to study the exact controllability without considering the compactness of the semigroup. An example is provided to highlight our main findings.</p>

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EXISTENCE AND EXACT CONTROLLABILITY FOR PERTURB EVOLUTION INCLUSIONS GOVERNED BY HILFER FRACTIONAL DERIVATIVES

  • 期刊论文

  • 发表日期：

    2025年8月27日

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  • Jayanta Borah,
  • Darshana Devi

摘要

In this article, we explore a category of semilinear perturb evolution inclusions that incorporate a nonlocal condition, specifically involving the Hilfer fractional derivative characterized by an order \(0< \epsilon < 1\) 0 < ϵ < 1 and type \(0 \le \rho \le 1\) 0 ≤ ρ ≤ 1 . Our approach focuses on proving the existence and exact controllability of solutions by applying well-established concepts in fractional calculus, set-valued mappings, and a hybrid fixed point theorem tailored for two operators. We find a different approach to study the exact controllability without considering the compactness of the semigroup. An example is provided to highlight our main findings.