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<p>This study explores the global Mittag-Leffler stability and finite time stability of incommensurate fractional-order inertial delay BAM neural networks. Initially, the system, characterized by high-order incommensurate fractional-order dynamics, is transformed into a low-order system through an appropriate variable substitution. Subsequently, sufficient conditions for the achievement of global Mittag-Leffler stability and finite time stability are derived. These conditions are based on the properties of the Riemann-Liouville fractional derivative and integral, and the relation of fractional integral inequalities to the Bellman-Gronwall inequality. The efficacy and accuracy of the proposed theoretical results are substantiated through two numerical simulations.</p>

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Two Types of Stability Criteria for Incommensurate Fractional-Order Inertial Delay BAM Neural Networks

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月6日

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  • Xu Danning,
  • Liu Wei

摘要

This study explores the global Mittag-Leffler stability and finite time stability of incommensurate fractional-order inertial delay BAM neural networks. Initially, the system, characterized by high-order incommensurate fractional-order dynamics, is transformed into a low-order system through an appropriate variable substitution. Subsequently, sufficient conditions for the achievement of global Mittag-Leffler stability and finite time stability are derived. These conditions are based on the properties of the Riemann-Liouville fractional derivative and integral, and the relation of fractional integral inequalities to the Bellman-Gronwall inequality. The efficacy and accuracy of the proposed theoretical results are substantiated through two numerical simulations.