  I In this work, we present the study of the regularity of the solutions of
the abstract system\eqref{Eq1.10} that includes the Euler-Bernoulli($\omega=0$)
and Kirchoff-Love($\omega>0$) thermoelastic plates, we consider for both
fractional couplings given by $A^\sigma\theta$ and $A^\sigma u_t$, where $A$ is
a strictly positive and self-adjoint linear operator and the parameter
$\sigma\in[0,\frac{3}{2}]$. Our research stems from the work of \cite{MSJR},
\cite{OroJRPata2013}, and \cite{KLiuH2021}. Our contribution was to directly
determine the Gevrey sharp classes: for $\omega=0$,
$s_{01}>\frac{1}{2\sigma-1}$ and $s_{02}> \sigma$ when $\sigma\in
(\frac{1}{2},1)$ and $\sigma\in (1,\frac{3}{2})$ respectively. And
$s_\omega>\frac{1}{4(\sigma-1)}$ for case $\omega>0$ when $\sigma\in
(1,\frac{5}{4})$. This work also contains direct proofs of the analyticity of
the corresponding semigroups $e^{t\mathbb{A}_\omega}$: In the case $\omega=0$
the analyticity of the semigroup $e^{t\mathbb{A}_0}$ occurs when $\sigma=1$ and
for the case $\omega>0$ the semigroup $e^{t\mathbb{A}_\omega}$ is analytic for
the parameter $\sigma\in[5/4, 3/2]$. The abstract system is given by:
\begin{equation}\label{Eq1.10} \left\{\begin{array}{c} u_{tt}+\omega
Au_{tt}+A^2u-A^\sigma\theta=0,\\ \theta_t+A\theta+A^\sigma u_t=0.
\end{array}\right. \end{equation} where $\omega\geq 0$.
