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Open Access Research Article

Exploring boundedness and oscillatory behaviour in impulsive stochastic fractional differential equations : Theoretical insights and practical applications

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pp. 1–25Online FirstJuly 2026DOI: 10.47974/JIM-2461XML
Received:
01 May 2025
Published Online:
15 Jul 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2461
Pages:
1–25

Abstract

This research focuses on Impulsive Stochastic Fractional Differential Equations (ISFDEs) with order α ∈ (0, 1) and discusses the role played by impulsivity and stochasticity in the system. Impulsivity means the sudden changes in the state of the system at certain moments, usually because of external shocks. On the other hand, stochasticity represents the random nature in the system, often described by stochastic processes, for example, Brownian motions. Stochastic differential equations provide a powerful framework to model randomness in dynamic systems [15]. Impulsive fractional integro-delay systems have been studied to capture sudden state changes in dynamic systems [9]. The research discusses the boundedness, oscillatory properties, and the existence of the solution for the ISFDEs. The results provide a theory for the understanding of the role played by the combination of fractional derivatives, impulsivity, and stochasticity in the system’s stability and long-term behavior. The results are applicable in control theory, biology, economics, and other fields, especially in the presence of sudden changes and random elements in the system. 

Keywords

Subject Classifications

34A0860H1034K4560H1534D2093E03

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