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

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 cont...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2023-06, Vol.22 (2), Article 49
Main Authors: Alkhazzan, Abdulwasea, Wang, Jungang, Tunç, Cemil, Ding, Xiaoli, Yuan, Zhanbin, Nie, Yufeng
Format: Article
Language:English
Subjects:
Continuity
Difference and Functional Equations
Differential equations
Dynamical Systems and Ergodic Theory
Fractional calculus
Mathematics
Mathematics and Statistics
Time
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Summary: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.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-023-00750-x