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<p>This article investigates the Lagrange <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-exponential stability (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-LES) and convergence of fractional-order quaternion-valued neural networks (FOQVNNs). Several sufficient conditions for <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-LES of FOQVNN are established using the Lyapunov approach and fractional-order differential inequalities. This article employs the real separation and Lyapunov direct methods to deal with FOQVNNs. The addressed system’s parameters determine the convergence rate. Two numerical examples with simulation results are shown to demonstrate the effectiveness and accuracy of the proposed theoretical results.</p>

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\(\alpha \)-exponential stability analysis of fractional-order quaternion-valued neural networks in Lagrange sense

  • 期刊论文

  • 发表日期：

    2025年12月18日

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  • Sapna Baluni,
  • Vijay K. Yadav,
  • Subir Das

摘要

This article investigates the Lagrange \(\alpha \) α -exponential stability ( \(\alpha \) α -LES) and convergence of fractional-order quaternion-valued neural networks (FOQVNNs). Several sufficient conditions for \(\alpha \) α -LES of FOQVNN are established using the Lyapunov approach and fractional-order differential inequalities. This article employs the real separation and Lyapunov direct methods to deal with FOQVNNs. The addressed system’s parameters determine the convergence rate. Two numerical examples with simulation results are shown to demonstrate the effectiveness and accuracy of the proposed theoretical results.