Existence, Uniqueness, and Averaging Principle for a Class of Fractional Neutral Itô–Doob Stochastic Differential Equations

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-03-04 DOI:10.1002/mma.10850

Mohamed Rhaima, Lassaad Mchiri, Abdellatif Ben Makhlouf

引用次数: 0

Abstract

This paper explores the existence, uniqueness, and averaging principles of neutral fractional stochastic Itô–Doob differential equations (NFSIDDEs). By utilizing the Picard iteration technique (PIT), we establish the existence and uniqueness of solutions. Additionally, we demonstrate the averaging principle for NFSIDDEs through the utilization of key inequalities, including the Gronwall and Hölder inequalities. Our findings contribute to a deeper understanding of the qualitative behavior and stability properties of NFSIDDEs, incorporating the fields of neutral fractional calculus, stochastic analysis, and classical inequalities.

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一类分数中立型随机微分方程的存在唯一性及平均原理Itô-Doob

本文探讨了中性分数阶随机Itô-Doob微分方程的存在性、唯一性和平均原理。利用Picard迭代技术（PIT），建立了解的存在唯一性。此外，我们通过利用关键不等式，包括Gronwall和Hölder不等式，展示了NFSIDDEs的平均原理。我们的发现有助于更深入地了解NFSIDDEs的定性行为和稳定性特性，包括中性分数微积分，随机分析和经典不等式领域。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.