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<p>We propose a new concept of stability, called here as “aggregated multi-stability”, which is based on multiple aggregation functions and also uses Mittag-Leffler and hypergeometric functions. This is inspired by the general framework of the Ulam, Hyers and Rassias types of stability, but differs in essence both in the multi-dependency of various aggregation functions and in choosing special functions to play the role of controllers. This notion is applied here to a class of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1245_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathfrak {J}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">J</mi> </math></EquationSource> </InlineEquation>-Hilfer fractional differential equations for which we identify sufficient conditions to guarantee its aggregated multi-stability.</p>

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Aggregated multi-stability for a class of \(\mathfrak {J}\)-Hilfer fractional differential equations via Mittag-Leffler and hypergeometric type functions

  • 期刊论文

  • 发表日期：

    2025年1月16日

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  • Safoura Rezaei Aderyani,
  • Luís P. Castro,
  • Reza Saadati,
  • Choonkil Park

摘要

We propose a new concept of stability, called here as “aggregated multi-stability”, which is based on multiple aggregation functions and also uses Mittag-Leffler and hypergeometric functions. This is inspired by the general framework of the Ulam, Hyers and Rassias types of stability, but differs in essence both in the multi-dependency of various aggregation functions and in choosing special functions to play the role of controllers. This notion is applied here to a class of \(\mathfrak {J}\) J -Hilfer fractional differential equations for which we identify sufficient conditions to guarantee its aggregated multi-stability.