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

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

Numerical Functional Analysis and Optimization 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

Numerical Functional Analysis and Optimization 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Numerical Functional Analysis and Optimization is a journal aimed at development and applications of functional analysis and operator-theoretic methods in numerical analysis, optimization and approximation theory, control theory, signal and image processing, inverse and ill-posed problems, applied and computational harmonic analysis, operator equations, and nonlinear functional analysis. Not all high-quality papers within the union of these fields are within the scope of NFAO. Generalizations and abstractions that significantly advance their fields and reinforce the concrete by providing new insight and important results for problems arising from applications are welcome. On the other hand, technical generalizations for their own sake with window dressing about applications, or variants of known results and algorithms, are not suitable for this journal. Numerical Functional Analysis and Optimization publishes about 70 papers per year. It is our current policy to limit consideration to one submitted paper by any author/co-author per two consecutive years. Exception will be made for seminal papers.