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Razumikhin-type stability theorems for functional fractional-order differential systems and applications

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  • Chen, Boshan
  • Chen, Jiejie

Abstract

In this paper, we studied the stability of functional fractional-order differential systems using a Lyapunov function and develop Razumikhin-type uniform stability and global uniform asymptotic stability theorems for functional fractional-order differential systems, which involve Riemann–Liouville and Caputo derivatives respectively. Two examples are given as application of our theorems.

Suggested Citation

  • Chen, Boshan & Chen, Jiejie, 2015. "Razumikhin-type stability theorems for functional fractional-order differential systems and applications," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 63-69.
    • Handle: RePEc:eee:apmaco:v:254:y:2015:i:c:p:63-69
    DOI: 10.1016/j.amc.2014.12.010
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    Cited by:

    1. Ning, Jinghua & Hua, Changchun, 2022. "H∞ output feedback control for fractional-order T-S fuzzy model with time-delay," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    2. Chen, Liping & Li, Xiaomin & Chen, YangQuan & Wu, Ranchao & Lopes, António M. & Ge, Suoliang, 2022. "Leader-follower non-fragile consensus of delayed fractional-order nonlinear multi-agent systems," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    3. Yao, Zichen & Yang, Zhanwen & Zhang, Yusong, 2021. "A stability criterion for fractional-order complex-valued differential equations with distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Ravi Agarwal & Snezhana Hristova & Donal O’Regan, 2021. "Stability Concepts of Riemann-Liouville Fractional-Order Delay Nonlinear Systems," Mathematics, MDPI, vol. 9(4), pages 1-16, February.
    5. Sakthivel, R. & Sweetha, S. & Tatar, N.E. & Panneerselvam, V., 2023. "Delayed reset control design for uncertain fractional-order systems with actuator faults via dynamic output feedback scheme," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    6. Aghayan, Zahra Sadat & Alfi, Alireza & Mousavi, Yashar & Kucukdemiral, Ibrahim Beklan & Fekih, Afef, 2022. "Guaranteed cost robust output feedback control design for fractional-order uncertain neutral delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    7. Zhang, Lingzhong & Yang, Yongqing & Wang, Fei, 2017. "Projective synchronization of fractional-order memristive neural networks with switching jumps mismatch," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 402-415.
    8. Peng, Qiu & Jian, Jigui, 2023. "Asymptotic synchronization of second-fractional -order fuzzy neural networks with impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    9. Chen, Juan & Zhou, Hua-Cheng & Zhuang, Bo & Xu, Ming-Hua, 2023. "Active disturbance rejection control to stabilization of coupled delayed time fractional-order reaction–advection–diffusion systems with boundary disturbances and spatially varying coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    10. Chen Chen & Qixiang Dong, 2022. "Existence and Hyers–Ulam Stability for a Multi-Term Fractional Differential Equation with Infinite Delay," Mathematics, MDPI, vol. 10(7), pages 1-15, March.
    11. Yang, Zhanwen & Li, Qi & Yao, Zichen, 2023. "A stability analysis for multi-term fractional delay differential equations with higher order," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    12. Ravi Agarwal & Snezhana Hristova & Donal O’Regan, 2022. "Generalized Proportional Caputo Fractional Differential Equations with Delay and Practical Stability by the Razumikhin Method," Mathematics, MDPI, vol. 10(11), pages 1-15, May.
    13. Wang, Fei & Zheng, Zhaowen & Yang, Yongqing, 2021. "Quasi-synchronization of heterogenous fractional-order dynamical networks with time-varying delay via distributed impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    14. Shafiya, M. & Nagamani, G. & Dafik, D., 2022. "Global synchronization of uncertain fractional-order BAM neural networks with time delay via improved fractional-order integral inequality," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 168-186.
    15. Fei Qi & Yi Chai & Liping Chen & José A. Tenreiro Machado, 2020. "Delay-Dependent and Order-Dependent Guaranteed Cost Control for Uncertain Fractional-Order Delayed Linear Systems," Mathematics, MDPI, vol. 9(1), pages 1-13, December.
    16. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun, 2017. "Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 416-422.
    17. Yao, Xueqi & Zhong, Shouming, 2021. "EID-based robust stabilization for delayed fractional-order nonlinear uncertain system with application in memristive neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    18. Li, Hong-Li & Jiang, Yao-Lin & Wang, Zuolei & Zhang, Long & Teng, Zhidong, 2015. "Global Mittag–Leffler stability of coupled system of fractional-order differential equations on network," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 269-277.

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