TIMOSHENKO SYSTEM WITH INTERNAL DISSIPATION OF FRACTIONAL DERIVATIVE TYPE

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.