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Fixed-time synchronization of fractional-order Hopfield neural networks with proportional delays

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  • Kumar, Pushpendra
  • Assali, El Abed

Abstract

This article explores the fixed-time synchronization of fractional-order Hopfield neural networks incorporating proportional delays. Unlike finite-time synchronization, where the convergence time varies based on the initial synchronization errors, fixed-time synchronization allows for a predetermined settling time that remains independent of initial conditions. To achieve fixed-time synchronization, two types of feedback control strategies incorporating fractional integrals are employed: one based on state feedback and another utilizing a controller designed with a Lyapunov function and an exponential function. By designing appropriate Lyapunov functions and employing inequality techniques, multiple sufficient conditions were established to guarantee the fixed-time synchronization of the considered systems under these control strategies. Finally, two numerical examples are presented to demonstrate the validity and practical relevance of the theoretical findings.

Suggested Citation

  • Kumar, Pushpendra & Assali, El Abed, 2026. "Fixed-time synchronization of fractional-order Hopfield neural networks with proportional delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 240(C), pages 367-380.
    • Handle: RePEc:eee:matcom:v:240:y:2026:i:c:p:367-380
    DOI: 10.1016/j.matcom.2025.07.035
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