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<p>In this paper we analyze an extensible Euler-Bernoulli beam equations in a bounded domain with a damping involving a Caputo time-fractional derivative. We consider an augmented model and we study some stability issues of this model. The existence and uniqueness of the solution are obtained by applying the semigroup theory. By following a result according to Arendt–Batty, we show that the linear semigroup is strongly stable. Ignoring geometric nonlinearity, we prove that the problem under consideration is not exponentially stable by an approach based on the Gearhart-Herbst-Prüss-Huang theorem. Then, by using a resolvent criterion developed by Borichev and Tomilov, we prove that the solutions decay polynomially with a decay rate depending on the value of the fractional damping orders.</p>

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Spectral analysis for coupled extensible Euler-Bernoulli beams with fractional derivative damping

  • 期刊论文

  • 发表日期：

    2026年5月19日

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  • Moncef Aouadi,
  • Taoufik Moulahi,
  • Najmeddine Attia,
  • Muneerah Al Nuwairan

摘要

In this paper we analyze an extensible Euler-Bernoulli beam equations in a bounded domain with a damping involving a Caputo time-fractional derivative. We consider an augmented model and we study some stability issues of this model. The existence and uniqueness of the solution are obtained by applying the semigroup theory. By following a result according to Arendt–Batty, we show that the linear semigroup is strongly stable. Ignoring geometric nonlinearity, we prove that the problem under consideration is not exponentially stable by an approach based on the Gearhart-Herbst-Prüss-Huang theorem. Then, by using a resolvent criterion developed by Borichev and Tomilov, we prove that the solutions decay polynomially with a decay rate depending on the value of the fractional damping orders.