On Existence and Continuity Results of Solution for Multi-time Scale Fractional Stochastic Differential Equation

Abdulwasea Alkhazzan ^[1] ; Jungang Wang ^[1] ; Cemil Tunç ^[3] ; Xiaoli Ding ^[2] ; Zhanbin Yuan ^[1] ; Yufeng Nie ^[1]
1. [1] Northwestern Polytechnical University
  
  Northwestern Polytechnical University
  
  China
2. [2] Xi'an Polytechnic University
  
  Xi'an Polytechnic University
  
  China
3. [3] Van Yuzuncu Yil University
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Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 2, 2023
Idioma: inglés
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Resumen
- In this paper, we study four critical aspects of a new class of multi-time scale nonlinear fractional stochastic differential equations with fractional integral in the sense of Riemann Liouville. A primary goal of this paper is to investigate the existence, uniqueness, Ulam-Hyers stability, and continuity of the solutions under sufficient assumptions using the Banach contraction theorem. At the end of the paper, a specific example is provided to demonstrate the efficiency and effectiveness of the new results of this paper.