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<p>This paper proposes new theoretical achievements about complete synchronization (CS) of discrete-time fractional-order neural networks with leakage and distributed delays (FNNLDDs). Firstly, some serviceable equations about Mittag-Leffler function are gained by Laplace transform and its properties. Secondly, an innovative discrete fractional Halanay inequality is obtained on the basis of fractional difference theory and some properties of Mittag-Leffler function. Then, by using Caputo fractional difference theory and associating with inequality derived herein, some sufficient CS criteria of discrete-time FNNLDDs are established under nonlinear feedback controller. Finally, a numerical example is given to certify effectiveness of the proposed theory in this paper.</p>

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Complete synchronization of discrete-time fractional-order neural networks with leakage and distributed delays

  • 期刊论文

  • 发表日期：

    2025年9月12日

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  • Jianfei Liu,
  • Hong-Li Li,
  • Yiheng Wei,
  • Yongguang Yu,
  • Jinde Cao

摘要

This paper proposes new theoretical achievements about complete synchronization (CS) of discrete-time fractional-order neural networks with leakage and distributed delays (FNNLDDs). Firstly, some serviceable equations about Mittag-Leffler function are gained by Laplace transform and its properties. Secondly, an innovative discrete fractional Halanay inequality is obtained on the basis of fractional difference theory and some properties of Mittag-Leffler function. Then, by using Caputo fractional difference theory and associating with inequality derived herein, some sufficient CS criteria of discrete-time FNNLDDs are established under nonlinear feedback controller. Finally, a numerical example is given to certify effectiveness of the proposed theory in this paper.