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

Ahmed Adnane, Abbes Benaissa, Khalida Benomar

• 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.