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<p>The well-known Halanay inequality is generalized here to the fractional-order case. We investigate this inequality in presence of a generalized Caputo fractional derivative in addition to discrete and distributed delays of not necessarily convolution type. The obtained result is then applied to a Hopfield Neural Network system to discuss its stability. This needs proving various lemmas on properties of the considered generalized Caputo derivative. We prove that solutions decay as a Mittag-Leffler function composed with a power function.</p>

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Halanay inequality involving \(\psi -\)Caputo derivative and application to a neural network system

  • 期刊论文

  • 发表日期：

    2025年10月7日

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  • Mohammed D. Kassim,
  • Nasser-eddine Tatar

摘要

The well-known Halanay inequality is generalized here to the fractional-order case. We investigate this inequality in presence of a generalized Caputo fractional derivative in addition to discrete and distributed delays of not necessarily convolution type. The obtained result is then applied to a Hopfield Neural Network system to discuss its stability. This needs proving various lemmas on properties of the considered generalized Caputo derivative. We prove that solutions decay as a Mittag-Leffler function composed with a power function.