New Stabilization Results for the One-Dimensional Fractional-Time Glycolysis Reaction-Diffusion System Through Neumann Boundary Feedback Controls

IF 2 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2026-10-07 Epub Date: 2026-08-11 DOI:10.1002/mma.70934

Feten Maddouri

引用次数: 0

Abstract

Stabilization of the linearized time fractional reaction-diffusion system in one-dimensional modeling glycolysis (LFRDG) has been rigorously studied. First, the nonlinear fractional reaction-diffusion (NLFRDG) system is linearized around a steady-state. Then, using semigroup theory on Banach spaces, we demonstrated that the LFRDG system with homogeneous Neumann boundary conditions admits a unique global solution. Furthermore, we have proven that such a solution is Mittag-Leffler (ML) stable. In the second part of this work, using a backstepping approach, we proved that there exists Neumann feedback boundary controls such that the LFRDG system is ML stable. In fact, the results obtained here are new in the context of the stabilization for the LFRDG models by Neumann-type boundary controls through the backstepping method. Finally, some numerical examples are presented to illustrate the theoretical results.

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一维分数时间糖酵解反应扩散系统的Neumann边界反馈稳定化新结果

对一维模拟糖酵解（LFRDG）中线性化时间分数反应扩散系统的稳定性进行了严格的研究。首先，将非线性分数阶反应扩散（NLFRDG）系统沿稳态线性化。然后，利用Banach空间上的半群理论，证明了具有齐次Neumann边界条件的LFRDG系统存在唯一全局解。此外，我们还证明了这种解决方案是Mittag-Leffler （ML）稳定的。在本工作的第二部分，我们使用回溯方法证明了存在Neumann反馈边界控制，使得LFRDG系统是ML稳定的。实际上，本文所得到的结果对于采用neumann型边界控制通过反演方法对LFRDG模型进行稳定化是新的。最后，通过数值算例对理论结果进行了验证。

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.