Regional Boundary Observability for Semilinear Fractional Systems with Riemann-Liouville Derivative

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-02-15 DOI:10.1080/01630563.2023.2171055

Khalid Zguaid, F. E. El Alaoui

引用次数: 2

Abstract

Abstract In this manuscript, we consider the problem of regional boundary observability for semilinear time-fractional systems involving the Riemann-Liouville fractional derivative. Our primary goal is to focus on reconstructing the initial state in the desired subregion located on the boundary of the spatial domain. To do that, we firstly construct a link between regional boundary observability of the considered semilinear system and regional observability of its linear part. And with the help of an extension of the Hilbert uniqueness method (HUM), we recover the value of the initial state on the desired boundary subregion. We also provide a numerical simulation based on the steps of the HUM approach that shows the proposed algorithm’s efficiency and backs up our theoretical results.

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具有Riemann-Liouville导数的半线性分数阶系统的区域边界可观测性

本文研究了黎曼-刘维尔分数阶导数的半线性时间分数阶系统的区域边界可观测性问题。我们的主要目标是专注于重建位于空间域边界的期望子区域的初始状态。为此，我们首先在所考虑的半线性系统的区域边界可观测性与其线性部分的区域可观测性之间建立了联系。利用Hilbert唯一性方法(HUM)的一种扩展，我们恢复了期望边界子区域上的初始状态值。我们还提供了一个基于HUM方法步骤的数值模拟，显示了所提出算法的效率并支持了我们的理论结果。

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

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.