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Exponential stabilization for spatial multiple-fractional advection-diffusion-reaction system

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  • Li, Xing-Yu
  • Wu, Kai-Ning
  • Yang, Zhan-Wen

Abstract

The exponential stabilization for spatial multiple-fractional advection-diffusion-reaction system (SMFADRS) is considered, and for the disturbed SMFADRS, the finite-time H∞ stabilization is investigated. To ensure the considered system to achieve the desired performance, a distributed controller is designed to be located in the sub-intervals of the whole spatial domain. Then, by deriving an improved fractional Poincare's inequality and resorting to the Lyapunov functional method, the sufficient criteria of exponential stability and finite-time H∞ performance are obtained. Besides, we also explore the effect of the space domain and its division, the control gain, the distribution of controller and the fractional order on the stability. Moreover, we apply the obtained theoretical results to address the control problem of the groundwater pollution, and the corresponding numerical simulations are performed to show the effectiveness of our results.

Suggested Citation

  • Li, Xing-Yu & Wu, Kai-Ning & Yang, Zhan-Wen, 2025. "Exponential stabilization for spatial multiple-fractional advection-diffusion-reaction system," Applied Mathematics and Computation, Elsevier, vol. 499(C).
    • Handle: RePEc:eee:apmaco:v:499:y:2025:i:c:s0096300325001365
    DOI: 10.1016/j.amc.2025.129409
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    References listed on IDEAS

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    1. Wu, Hao & Hu, Junhao & Yuan, Chenggui, 2022. "Stability of numerical solution to pantograph stochastic functional differential equations," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    2. Jin, Ting & Sun, Yun & Zhu, Yuanguo, 2020. "Time integral about solution of an uncertain fractional order differential equation and application to zero-coupon bond model," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    3. Jia, Jinping & Dai, Hao & Li, Li & Zhang, Fandi, 2021. "Global sampled-data stabilization for a class of nonlinear systems with arbitrarily long input delays via a multi-rate control algorithm," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    4. Guo, Mengyu & Wang, Peiguang, 2024. "Finite-time stability of non-instantaneous impulsive systems with double state-dependent delays," Applied Mathematics and Computation, Elsevier, vol. 477(C).
    5. Li, Zhao-Yan & Zhang, Qianqian & Zhou, Bin, 2024. "On exponential and L2-exponential stability of continuous-time delay-difference systems," Applied Mathematics and Computation, Elsevier, vol. 481(C).
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