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<p>This paper investigates a nonlinear initial value problem involving the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11565_2025_607_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varphi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation>-Caputo fractional derivative within the framework of a Banach space. To establish the existence of mild solutions, we utilize the Meir-Keeler fixed point theorem in conjunction with the concept of measure of noncompactness. The existence and uniqueness of solutions are further demonstrated via the Banach contraction principle. In addition, we explore the solution’s sensitivity to initial data and examine its Ulam-Hyers stability. To illustrate the theoretical findings, representative examples are presented.</p>

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On the solvability and stability of nonlinear \(\varphi \)-Caputo fractional differential equations in Banach spaces

  • 期刊论文

  • 发表日期：

    2025年8月12日

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  • Mohammed Messous,
  • Hana Aouadjia,
  • Abdelouaheb Ardjouni,
  • Ali Rezaiguia

摘要

This paper investigates a nonlinear initial value problem involving the \(\varphi \) φ -Caputo fractional derivative within the framework of a Banach space. To establish the existence of mild solutions, we utilize the Meir-Keeler fixed point theorem in conjunction with the concept of measure of noncompactness. The existence and uniqueness of solutions are further demonstrated via the Banach contraction principle. In addition, we explore the solution’s sensitivity to initial data and examine its Ulam-Hyers stability. To illustrate the theoretical findings, representative examples are presented.