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<p>In this manuscript, we investigated the existence, uniqueness, and Ulam–Hyers stability results of solutions to implicit Caputo–Hadamard fractional differential equations with noninstantaneous impulses and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2024_1958_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="109" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>δ</mi> <mo>−</mo> <mi>d</mi> <mi>e</mi> <mi>r</mi> <mi>i</mi> <mi>v</mi> <mi>a</mi> <mi>t</mi> <mi>i</mi> <mi>v</mi> <mi>e</mi> </math></EquationSource> <EquationSource Format="TEX">$\delta -derivative$</EquationSource> </InlineEquation> initial conditions. By employing Banach’s and Schaefer’s fixed-point theorems, we attain the required results. Finally, we provide examples that support the main findings we arrived at.</p>

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Existence and Ulam–Hyers stability results for Caputo–Hadamard fractional differential equations with non-instantaneous impulses

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月14日

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  • Mesfin Teshome Beyene,
  • Mitiku Daba Firdi,
  • Tamirat Temesgen Dufera

摘要

In this manuscript, we investigated the existence, uniqueness, and Ulam–Hyers stability results of solutions to implicit Caputo–Hadamard fractional differential equations with noninstantaneous impulses and δ − d e r i v a t i v e $\delta -derivative$ initial conditions. By employing Banach’s and Schaefer’s fixed-point theorems, we attain the required results. Finally, we provide examples that support the main findings we arrived at.