<p>In this paper, we consider the stability and regularity of a coupled plates transmission system with fractional rotational force and fractional damping. The rotational force and damping involve spectral fractional Laplacian operator, whose powers are in (0,&#xa0;1] and [0,&#xa0;2] respectively. We use the frequency domain method and multiplier technique to obtain the stability of the system. Here, we are interested in the stability of the coupled plates system when fractional damping acting on two plate equations simultaneously or only on one plate equation. It is find that the system decays to zero exponentially or polynomially, in which the fractional rotational force and the wave velocities also play important roles. We prove that the decay rates of polynomials obtained are all optimal. The obtained stability results indicate that the presence of higher fractional inertia term has a negative effect on the stability of the system, while the presence of higher fractional damping has a positive effect on the stability of the system. For the order of fractional rotational force is fixed, when fractional damping of the same order is added to equation with fractional inertia term instead of added to equation without fractional inertia term, the system exhibits better stability, which give us the control methods for designing stabilizers of plate coupled systems, and provide a theoretical basis for the design of stabilizers. In addition, we obtain the regularity results when fractional damping acting on two plate equations simultaneously, including the lacks of analytic, the lacks of Gevrey class, analytic, Gevrey class of the corresponding semigroup, and give the orders of Gevrey class. This paper extends the results of previous studies. Transmission systems for coupled plates with fractional damping arise in the fields of physics, mechanics and electronic circuit, etc. So the obtained results have important theoretical and practical significance.</p>