The Solvability and Sensitivity of Nonautonomous Fractional Differential Inclusions Steered by Mixed Brownian Motion

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-19 DOI:10.1002/mma.10712

Surendra Kumar, Anjali Upadhyay

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引用次数: 0

Abstract

The qualitative study of stochastic fractional nonautonomous systems in infinite-dimensional spaces is rarely available in the literature. Our aim in this article is to examine the existence and sensitivity of a mild solution for a novel class of nonautonomous stochastic fractional differential inclusions driven by standard and fractional Brownian motion (fBm). We derive the existence and uniqueness of the solution for the considered system with the help of operators generated by the probability density function and the family of linear, closed operators by utilizing the Picard iteration method. Furthermore, we investigate the sensitivity of the mild solution concerning the initial condition. The obtained results are proved under weaker assumptions than the Lipschitz conditions on the system parameters. We also use the Jensen, the Gronwall, and the Bihari inequalities to acquire the results. Our results generalize the work corresponding to fractional autonomous and deterministic systems. Lastly, two examples are constructed to validate the produced results.

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关于无穷维空间中随机分数非自治系统的定性研究在文献中很少见。本文旨在研究由标准和分数布朗运动（fBm）驱动的一类新型非自治随机分数微分夹杂的温和解的存在性和敏感性。我们借助由概率密度函数和线性封闭算子族产生的算子，利用皮卡尔迭代法推导出所考虑系统的解的存在性和唯一性。此外，我们还研究了温和解对初始条件的敏感性。所获得的结果是在比系统参数的 Lipschitz 条件更弱的假设条件下证明的。我们还使用了詹森、格伦沃尔和比哈里不等式来获得结果。我们的结果推广了与分数自治系统和确定性系统相对应的工作。最后，我们构建了两个实例来验证所得出的结果。

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.