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<p>This paper aims to examine the existence, uniqueness, and stability properties of a novel category of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2039_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="7" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">f</mi> </math></EquationSource> <EquationSource Format="TEX">$\mathfrak{f}$</EquationSource> </InlineEquation>-Caputo generalized proportional differential equations characterized by two distinct fractional orders. We explore and discuss various properties of the generalized proportional operator. Using the Schaefer fixed point theorem and the Banach contraction principle, we establish results on existence and uniqueness, along with different types of stabilities, including Ulam-Hyers and generalized Ulam-Hyers stability. An example is provided to complete the numerical validation of the theoretical results.</p>

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Existence, uniqueness and stability analysis for a \(\mathfrak{f}\)-Caputo generalized proportional fractional boundary problem with distinct generalized integral conditions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月7日

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  • Hamid Lmou,
  • Samira Zerbib,
  • Sina Etemad,
  • İbrahim Avcı,
  • Raaid Alubady

摘要

This paper aims to examine the existence, uniqueness, and stability properties of a novel category of f $\mathfrak{f}$ -Caputo generalized proportional differential equations characterized by two distinct fractional orders. We explore and discuss various properties of the generalized proportional operator. Using the Schaefer fixed point theorem and the Banach contraction principle, we establish results on existence and uniqueness, along with different types of stabilities, including Ulam-Hyers and generalized Ulam-Hyers stability. An example is provided to complete the numerical validation of the theoretical results.