Uniform stabilization for a Timoshenko beam system with delays in fractional order internal dampings

Ahmed Adnane ^[1] ; Abbes Benaissa ^[1] ; Khalida Benomar ^[1]
1. [1] Laboratory of Analysis and Control of PDEs, Djillali Liabes University
Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 80, Nº. 2, 2023, págs. 283-302
Idioma: inglés
DOI: 10.1007/s40324-022-00286-1
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Resumen
- This work is concerned with a problem of a vibrating system of Timoshenko-type in a bounded one-dimensional domain under Dirichlet boundary conditions with two fractional time delays and two internal frictional dampings. Under a smallness condition on the fractional delay and by using a classical semigroup theory we prove existence and uniqueness of solutions. Furthermore, by a frequency domain approach we prove an exponential stability result.