Polynomial stability of a Kirchhoff plate equation in the presence of a frictional damping, a fractional time delay, and a source term

We investigate the asymptotic behavior of a Kirchhoff plate equation with free boundary conditions in a bounded domain of ${\mathbb{R}}^2$ $\mathbb{R}^{2}$ . The model involves frictional internal damping, a time delay condition of fractional type and a source term. We derive a polynomial decay estimate for the associated semigroup by using the frequency domain method.