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Uniform boundedness and stability of fractional state-dependent delayed systems and applications to complex neural networks

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  • Xu, Liguang
  • Hu, Hongxiao
  • He, Danhua

Abstract

In this article, the uniform boundedness and stability are investigated for a class of conformable fractional state-dependent delayed nonlinear systems. First, the definitions of generalized conformable fractional derivative and integral with subscripts are presented along with their properties, which improve and generalize the existing ones. Second, a conformable fractional exponential function inequality and a non-autonomous conformable fractional differential inequality are established, which can overcome the difficulties caused by fractional differential operators. Third, by combining the method of proof by contradiction with the Lyapunov method and the obtained inequalities, sufficient conditions are derived to ensure the uniform boundedness and stability of the addressed systems. Our results include some existing works on integer-order systems as special cases. Furthermore, as an application, the obtained theoretical results are applied to the quasi-synchronization problem of conformable fractional complex neural networks. Finally, examples are also provided to show the effectiveness of the theoretical results.

Suggested Citation

  • Xu, Liguang & Hu, Hongxiao & He, Danhua, 2026. "Uniform boundedness and stability of fractional state-dependent delayed systems and applications to complex neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 599-615.
    • Handle: RePEc:eee:matcom:v:239:y:2026:i:c:p:599-615
    DOI: 10.1016/j.matcom.2025.06.018
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    References listed on IDEAS

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    1. Tran Nguyen Binh & Nguyen Huu Sau & Nguyen Thi Thanh Huyen & Mai Viet Thuan, 2025. "Guaranteed cost control of delayed conformable fractional-order systems with nonlinear perturbations using an event-triggered mechanism approach," International Journal of Systems Science, Taylor & Francis Journals, vol. 56(12), pages 2991-3008, September.
    2. Hashemi, M.S., 2018. "Invariant subspaces admitted by fractional differential equations with conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 161-169.
    3. Chu, Xiaoyan & Xu, Liguang & Hu, Hongxiao, 2020. "Exponential quasi-synchronization of conformable fractional-order complex dynamical networks," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Silva, Cristiana J. & Torres, Delfim F.M., 2019. "Stability of a fractional HIV/AIDS model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 164(C), pages 180-190.
    5. Xu, Liguang & Chu, Xiaoyan & Hu, Hongxiao, 2021. "Quasi-synchronization analysis for fractional-order delayed complex dynamical networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 594-613.
    6. Yu, Nanxiang & Zhu, Wei, 2021. "Event-triggered impulsive chaotic synchronization of fractional-order differential systems," Applied Mathematics and Computation, Elsevier, vol. 388(C).
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