Effects of Lévy noise and impulsive action on the averaging principle of Atangana–Baleanu fractional stochastic delay differential equations

IF 1.7 4区 数学 Q1 Mathematics Boundary Value Problems Pub Date : 2024-07-25 DOI:10.1186/s13661-024-01898-4
A. M. Sayed Ahmed, Hamdy M. Ahmed, Karim K. Ahmed, Farah M. Al-Askr, Wael W. Mohammed
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Abstract

As delays are common, persistent, and ingrained in daily life, it is imperative to take them into account. In this work, we explore the averaging principle for impulsive Atangana–Baleanu fractional stochastic delay differential equations driven by Lévy noise. The link between the averaged equation solutions and the equivalent solutions of the original equations is shown in the sense of mean square. To achieve the intended outcomes, fractional calculus, semigroup properties, and stochastic analysis theory are used. We also provide an example to demonstrate the practicality and relevance of our research.
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莱维噪声和脉冲作用对阿坦加纳-巴莱阿努分数随机延迟微分方程平均原理的影响
由于延迟是日常生活中常见、持久和根深蒂固的现象,因此必须将其考虑在内。在这项研究中,我们探讨了由 Lévy 噪声驱动的脉冲 Atangana-Baleanu 分数随机延迟微分方程的平均原理。平均方程解与原方程等效解之间的联系是在均方意义上显示出来的。为了达到预期结果,我们使用了分数微积分、半群性质和随机分析理论。我们还提供了一个示例来证明我们研究的实用性和相关性。
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来源期刊
Boundary Value Problems
Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.00
自引率
5.90%
发文量
83
审稿时长
4 months
期刊介绍: The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.
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