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In this work we study a strongly coupled system between the equation ofplates with fractional rotational inertial force $\kappa(-\Delta)^\beta u_{tt}$where the parameter $0 <\beta\leq 1$ and the equation of an electrical networkcontaining a fractional dissipation term $\delta(-\Delta)^\theta v_t$ where theparameter $0\leq \theta\leq 1$, the strong coupling terms are given by theLaplacian of the displacement speed $\gamma \Delta u_t$ and the Laplacianelectric potential field $\gamma\Delta v_t$. When $\beta = 1$, we have theKirchoff-Love plate and when $\beta = 0$, we have the Euler-Bernoulli platerecently studied in Su\'arez-Mendes (2022-Preprinter)\cite{Suarez}. Thecontributions of this research are: We prove the semigroup $S(t)$ associatedwith the system is not analytic in $(\theta,\beta)\in [0,1]\times(0,1]-\{(1,1/2)\}$. We also determine two Gevrey classes: $s_1 >\frac{1}{2\max\{\frac{1-\beta}{3-\beta}, \frac{\theta}{2+\theta-\beta}\}}$ for $2\leq\theta+2\beta$ and $s_2> \frac{2(2+\theta-\beta)}{\theta}$ when the parameters$\theta$ and $\beta$ lies in the interval $(0, 1)$ and we finish by provingthat at the point $(\theta,\beta)=(1,1/2)$ the semigroup $S(t)$ is analytic andwith a note about the asymptotic behavior of $S(t)$. We apply semigroup theory,the frequency domain method together with multipliers and the properdecomposition of the system components and Lions' interpolation inequality.

The regularity of the coupled system between an electrical network with  fractional dissipation and a plate equation with fractional inertial  rotational