On the Cauchy Problem for Nonlinear Fractional Systems with Lipschitzian Matrices Under the Generalized Metric Spaces

• Abdelatif Boutiara ^[1] ; Sotiris K. Ntouyas ^[2] ; Taghreed A. Assiri ^[3] ; Jessada Tariboon ^[5] ; Emad E. Mahmoud ^[4]
  1. [1] University of Ghardaia

     University of Ghardaia

     Argelia

     
  2. [2] University of Ioannina

     University of Ioannina

     Dimos Ioánnina, Grecia

     
  3. [3] Umm al-Qura University

     Umm al-Qura University

     Arabia Saudí

     
  4. [4] Taif University

     Taif University

     Arabia Saudí

     
  5. [5] King Mongkut’s University of Technology North Bangkok

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-01127-4
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• Resumen

  • This research paper study the existence, uniqueness and Ulam–Hyers stability of the solutions of a certain system of thegeneralized Caputo fractional differential equations in the context of the generalized metric spaces. The existence and uniqueness theorems are proved by using the Krasnoselskii’s and Perov’s fixed point theorems under the Bielecki norm with a Lipschitzian matrix in the generalized metric spaces. Moreover, the Ulam–Hyers stability analysis is conducted based on the Urs’s criterion. An example, lastly, is proposed to check the efficiency of the above-mentioned theorems.

    The results are novel and provide extensions to some of the findings known in the literature.

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