<p>This study explores a new type of impulsive nonlocal Caputo fractional dynamical differential inclusions of order <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2412_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="72" /> </InlineMediaObject> <EquationSource Format="TEX">\(1&lt; \varrho &lt; 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>&lt;</mo> <mi>ϱ</mi> <mo>&lt;</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> in Banach space. The major goal is to identify mild solutions for impulsive nonlocal Caputo fractional Volterra–Fredholm integrodifferential inclusions with infinite delay. We use methods from fractional calculus, Dhage’s fixed-point concepts, integrodifferential equations, abstract phase space <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2412_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathscr {B}}_{g}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">B</mi> <mi>g</mi> </msub> </math></EquationSource> </InlineEquation>, multivalued analysis, and sectorial operator of type <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2412_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="76" /> </InlineMediaObject> <EquationSource Format="TEX">\((P, \kappa , \varrho , \gamma )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>P</mi> <mo>,</mo> <mi>κ</mi> <mo>,</mo> <mi>ϱ</mi> <mo>,</mo> <mi>γ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> to establish the necessary circumstances for the existence of mild solutions to these problems. Illustrative examples are provided to support the theoretical results and demonstrate their practical application.</p>

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Higher-order caputo fractional integrodifferential inclusions of Volterra–Fredholm type with impulses and infinite delay: existence results

  • Marimuthu Mohan Raja,
  • Velusamy Vijayakumar,
  • Kalyana Chakravarthy Veluvolu

摘要

This study explores a new type of impulsive nonlocal Caputo fractional dynamical differential inclusions of order \(1< \varrho < 2\) 1 < ϱ < 2 in Banach space. The major goal is to identify mild solutions for impulsive nonlocal Caputo fractional Volterra–Fredholm integrodifferential inclusions with infinite delay. We use methods from fractional calculus, Dhage’s fixed-point concepts, integrodifferential equations, abstract phase space \({\mathscr {B}}_{g}\) B g , multivalued analysis, and sectorial operator of type \((P, \kappa , \varrho , \gamma )\) ( P , κ , ϱ , γ ) to establish the necessary circumstances for the existence of mild solutions to these problems. Illustrative examples are provided to support the theoretical results and demonstrate their practical application.