Relative Controllability and Hyers–Ulam Stability of Riemann–Liouville Fractional Delay Differential System

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-04 DOI:10.1007/s12346-024-01046-4

Wangmin An, Danfeng Luo, Jizhao Huang

引用次数: 0

Abstract

In this work, we focus on the relative controllability and Hyers–Ulam stability of Riemann–Liouville fractional delay differential system of order \(\alpha \in (1,2)\). Firstly, for the linear system based on Mittag-Laffler matrix function, we define a controllability Grammian matrix to judge whether the system is relatively controllable. Additionally, with the aid of Krasnoselskii’s fixed point theorem, sufficient conditions for the relative controllability of the corresponding semilinear system is also studied. Furthermore, we used Grönwall’s inequality to investigate Hyers–Ulam stability for Riemann–Liouville fractional semilinear delay differential equations. Lastly, three instances are provided to verify that our theoretical results are accurate.

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黎曼-刘维尔分数延迟微分系统的相对可控性和海尔-乌兰稳定性

在这项工作中，我们主要研究阶数为\(α \in (1,2)\)的Riemann-Liouville分数延迟微分系统的相对可控性和Hyers-Ulam稳定性。首先，对于基于 Mittag-Laffler 矩阵函数的线性系统，我们定义了可控性 Grammian 矩阵来判断系统是否相对可控。此外，借助 Krasnoselskii 定点定理，我们还研究了相应半线性系统相对可控性的充分条件。此外，我们还利用格伦沃不等式研究了黎曼-刘维尔分数半线性延迟微分方程的海尔-乌兰稳定性。最后，我们提供了三个实例来验证我们的理论结果是准确的。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.