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September 10, 2025Filomat13 citationsOpen Access

Stability of hybrid differential equations in the sense of Hyers-Ulam using Gronwall lemma

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RSRahim ShahNINatasha IrshadDLDhaou Lassoued

Key Points

  • The research demonstrates a new framework for understanding hybrid differential equations.
  • Using Gronwall's lemma, the study establishes both Hyers-Ulam and Hyers-Ulam-Rassias stability.
  • Two examples are introduced to validate the proposed method and illustrate its effectiveness.
  • Graphical representations underscore the results, providing visual clarity on complex concepts.

Abstract

In this paper, for the first time, we use Gronwall?s lemma to show the Hyers-Ulam and Hyers-Ulam-Rassias stability of hybrid differential equations, offering a fresh and rigorous framework for studying these complex structures. Two examples are provided to illustrate the correctness of our method, and graphical illustrations are used to graphically represent the results.

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Cite This Study

Shah et al. (2025) studied this question.

synapsesocial.com/papers/68c1a11f54b1d3bfb60dbb48https://doi.org/10.2298/fil2504407s
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Ulam-Hyers-Rassias stability of pseudoparabolic partial differential equations2015 · 18 citations
  2. 2Hyers–Ulam stability of hypergeometric differential equations2018 · 51 citations
  3. 3On the Stability of the Linear Functional Equation1941 · 4,003 citations
  4. 4Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis2011 · 678 citations
  5. 5Sequential Caputo–Hadamard Fractional Differential Equations with Boundary Conditions in Banach Spaces2022 · 9 citations