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Study exponential and polynomial stability of Timoshenko beam with boundary dissipative conditions of fractional derivative type

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Abstract

In this paper, we consider the Timoshenko beam with only one dynamic control boundary condition of fractional derivative type. We show that the system is not uniformly stable by a spectrum method but it is polynomial stable using the frequency domain approach and Borichev and Tomilov’s result. These results improve some recent results in the literature.

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  1. C. Messikh and S. Labidi have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Badji Mokhtar University, 23000, B.P.12, Annaba, Algeria

    C. Messikh & S. Labidi

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  1. C. Messikh
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  2. S. Labidi
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Correspondence to C. Messikh.

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Messikh, C., Labidi, S. Study exponential and polynomial stability of Timoshenko beam with boundary dissipative conditions of fractional derivative type. Rend. Circ. Mat. Palermo, II. Ser 72, 673–706 (2023). https://doi.org/10.1007/s12215-021-00711-w

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  • DOI: https://doi.org/10.1007/s12215-021-00711-w

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