Qualitative Analysis of Impulsive Stochastic Hilfer Fractional Differential Equation

• Hamza Khalil ^[1] ; Akbar Zada ^[1] ; Sana Ben Moussa ^[2] ; Ioan-Lucian Popa ^[3] ; Afef Kallekh ^[2]
  1. [1] University of Peshawar

     University of Peshawar

     Pakistán

     
  2. [2] King Khalid University

     King Khalid University

     Arabia Saudí

     
  3. [3] University of Alba Iulia & Transilvania University of Brasov

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-01149-y
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• Resumen

  • This paper proves the qualitative properties like existence, uniqueness and Ulam- Hyers-Rassias stability for a solution of a nonlinear impulsive Hilfer fractional stochastic differential equation with non-instantaneous impulses. The Banach fixed point theorem and Cauchy inequality are utilized for obtaining our results. The Ulam-Hyers-Rassias stability is presented under specific assumptions. To verify the theoretical results an example is presented at the end.

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