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Adaptive synchronization of fractional-order complex networks involving non-differentiable time-varying delays

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  • Wang, Wenbo
  • Du, Feifei

Abstract

In this paper, the synchronization problem of fractional-order complex networks (FOCNs) involving non-differentiable time-varying delays is investigated and two novel adaptive control strategies are proposed. The boundedness of fractional-order adaptive controller gains, while crucial for engineering applications, presents unresolved challenges owing to the non-locality inherent in fractional-order calculus. To address this challenge, a synchronization criterion for centralized adaptive control of FOCNs involving non-differentiable time-varying delays is established by employing the fractional-order Halanay inequality. Moreover, the boundedness of the controller gains is proved via the property of the Mittag-Leffler function. Furthermore, by utilizing the Riemann Liouville integral property of function and the fractional-order Halanay inequality with a perturbation function, a synchronization criterion for decentralized adaptive control of FOCNs involving non-differentiable time-varying delays is developed. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Suggested Citation

  • Wang, Wenbo & Du, Feifei, 2026. "Adaptive synchronization of fractional-order complex networks involving non-differentiable time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 240(C), pages 226-237.
    • Handle: RePEc:eee:matcom:v:240:y:2026:i:c:p:226-237
    DOI: 10.1016/j.matcom.2025.07.015
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