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<p>In this paper, we analyze the stability of the fractional distributed delay models. We use the linear chain trick to convert these models into an incommensurate fractional order systems. We get the stability regions by studying the characteristic equation around equilibrium points. We investigate how the fractional order <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha _{1}\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\rho\)</EquationSource> </InlineEquation> and <i>a</i> affect the stability of the models. We study the fractional order delay logistic equation and compare the influence of the distributed delay on the stability regions. Numerical simulations are exhibited to confirm the analytical results.</p>

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Dynamic analysis of the fractional distributed delay models

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月26日

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  • H. A. A. El-Saka,
  • D. El. A. El-Sherbeny,
  • A. M. A. El-Sayed

摘要

In this paper, we analyze the stability of the fractional distributed delay models. We use the linear chain trick to convert these models into an incommensurate fractional order systems. We get the stability regions by studying the characteristic equation around equilibrium points. We investigate how the fractional order \(\alpha _{1}\) , \(\rho\) and a affect the stability of the models. We study the fractional order delay logistic equation and compare the influence of the distributed delay on the stability regions. Numerical simulations are exhibited to confirm the analytical results.