Fractional Timoshenko beam with a viscoelastically damped rotational component

This paper is concerned with a fractional Timoshenko system of order between one and two. We address the question of well-posedness in an appropriate space when the rotational component is viscoelastic or subject to a viscoelastic controller. To this end we use the notion of alpha-resolvent. Moreover, we prove that the memory term alone may stabilize the system in a Mittag-Leffler fashion. The system is Lyapunov stable or uniformly stable in the case of different speeds of propagation.