Existence and Optimal Controls for Generalized Riemann–Liouville Fractional Sobolev-Type Stochastic Integrodifferential Equations of Order ϑ∈(1,2)

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-05 DOI:10.1002/mma.10662

M. Johnson, V. Vijayakumar, Kiwoon Kwon

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引用次数: 0

Abstract

This manuscript addresses the optimal control of generalized Riemann–Liouville fractional (Hilfer fractional) Sobolev-type stochastic differential equations of order $ϑ \in (1, 2)$ in separable Hilbert spaces. First, the existence of mild solutions for the system is established using the cosine family of operators and the Leray–Schauder fixed point theorem. Then, the existence of optimal control is demonstrated through Balder's theorem. Finally, an example is provided to illustrate the results.

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广义Riemann-Liouville分数阶sobolev型随机积分微分方程的存在性及最优控制

本文研究了可分离Hilbert空间中阶为φ∈(1,2)$$ \vartheta \in \kern0.3em \left(1,2\right) $$的广义Riemann-Liouville分数（Hilfer分数）sobolev型随机微分方程的最优控制问题。首先，利用余弦算子族和Leray-Schauder不动点定理，建立了系统温和解的存在性。然后，利用Balder定理证明了最优控制的存在性。最后，给出了一个算例来说明结果。

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.