Shear Beam Model with Fractional Derivative-Type Internal Dissipation

Abstract

This work deals with the well-posedness and asymptotic behavior of a Shear beam model subject to internal dissipation of the fractional derivative-type. The energy functional is presented, and the dissipative property of the system is stablished. We use the semigroup theory in order to deal with the well-posedness and we prove the strong stability of the \(C_{0}\)-semigroup using the Arendt-Batty and Lyubich-Vũ’s general criterion and also we prove the polynomial stability result applying Borichev and Tomilov’s theorem.