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Mittag-Leffler ultimate boundedness of fractional-order nonautonomous delay systems

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  • Bao, Baizeng
  • Xu, Liguang

Abstract

This paper investigates the Mittag-Leffler ultimate boundedness of fractional-order nonautonomous systems with delay. First, using the properties of the Mittag-Leffler function and the fractional-order comparison principle, a novel fractional-order nonautonomous Halanay inequality is proposed, which no longer requires the conditions of boundedness and common factors of the coefficients of the systems. This implies that the conditions are less conservative than the existing results. Then, with the help of the obtained inequality, some criteria for the Mittag-Leffler ultimate boundedness of the considered system are derived. Finally, examples are given to demonstrate the effectiveness of the findings.

Suggested Citation

  • Bao, Baizeng & Xu, Liguang, 2025. "Mittag-Leffler ultimate boundedness of fractional-order nonautonomous delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:chsofr:v:197:y:2025:i:c:s0960077925004953
    DOI: 10.1016/j.chaos.2025.116482
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    References listed on IDEAS

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    1. Wang, Fei & Yang, Yongqing, 2018. "Quasi-synchronization for fractional-order delayed dynamical networks with heterogeneous nodes," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 1-14.
    2. Baizeng Bao & Hongxiao Hu & Liguang Xu, 2024. "Quasi-synchronisation of conformable fractional-order complex dynamical networks with mixed delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 55(14), pages 2996-3016, October.
    3. Liguang Xu & Baizeng Bao & Hongxiao Hu, 2025. "Stability of impulsive delayed switched systems with conformable fractional-order derivatives," International Journal of Systems Science, Taylor & Francis Journals, vol. 56(6), pages 1271-1288, April.
    4. Wang, Feng-Xian & Zhang, Jie & Shu, Yan-Jun & Liu, Xin-Ge, 2023. "On stability and event trigger control of fractional neural networks by fractional non-autonomous Halanay inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
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