TIMOSHENKO SYSTEM WITH INTERNAL DISSIPATION OF FRACTIONAL DERIVATIVE TYPE

Rafael Oliveira de Jesus; Carlos Alberto Raposo; Joilson Oliveira Ribeiro; Octavio Vera Villagran

doi:10.11948/20240289

2025 Volume 15 Issue 2

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Rafael Oliveira de Jesus, Carlos Alberto Raposo, Joilson Oliveira Ribeiro, Octavio Vera Villagran. TIMOSHENKO SYSTEM WITH INTERNAL DISSIPATION OF FRACTIONAL DERIVATIVE TYPE[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 1146-1169. doi: 10.11948/20240289

Citation:

Rafael Oliveira de Jesus, Carlos Alberto Raposo, Joilson Oliveira Ribeiro, Octavio Vera Villagran. TIMOSHENKO SYSTEM WITH INTERNAL DISSIPATION OF FRACTIONAL DERIVATIVE TYPE[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 1146-1169. doi: 10.11948/20240289

TIMOSHENKO SYSTEM WITH INTERNAL DISSIPATION OF FRACTIONAL DERIVATIVE TYPE

1.
Departament of Mathematics, University of Pernambuco, 56328-900, Petrolina-PE, Brazil
2.
Faculty of Mathematics, Federal University of Pará, 68721-000, Salinópolis-PA, Brazil
3.
Departament of Mathematics, Federal University of Bahia, 40170-110, Salvador-BA, Brazil
4.
Department of Mathematics, University of Tarapaca, Arica, Chile

Author Bio: Email: rafael.oliveira@upe.br(R. O. Jesus); Email: joilsonor@ufba.br(J. O. Ribeiro); Email: opverav@academicos.uta.cl(O. V. Villagran)
Corresponding author: Email: carlosraposo@ufpa.br(C. A. Raposo)

Abstract

Abstract

This manuscript deals with the well-posedness and asymptotic behavior of the Timoshenko system with internal dissipation of fractional derivative type. We use semigroup theory. The existence and uniqueness of the solution are obtained by applying the Lumer-Phillips Theorem. We present two results for the asymptotic behavior: strong stability of the $ C_{0} $-semigroup associated with the system using the Arendt-Batty and Lyubich-Vũ's general criterion and the polynomial stability applying the Borichev-Tomilov's theorem. This results expand the understanding of the asymptotic behavior of Timoshenko systems with fractional internal dissipation, providing clear criteria for both strong and polynomial stability.
- Timoshenko system /
- well-posedness /
- polynomial stability /
- fractional derivative type damping
MSC: 26A33, 35Q70, 35A01, 35B40

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References

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