In this talk, I'll investigate the stability of three models of systems. In the first and the second models, a Euler-Bernoulli beam and a wave equations coupled via boundary connections is considered. The localized non-smooth fractional Kelvin-Voigt damping acts through one of the two equations only, its effect is transmitted to the other equation through the coupling by boundary connections. In these two models, we reformulate the system into an augmented model and using a general criteria of Arendt-Batty, we show that the system is strongly stable. For the first model, where the dissipation acts through the wave equation, by using frequency domain approach, combined with multiplier technique we prove that the energy decays polynomially with rate t^{frac{-4}{2- α }} . For the second model, the dissipation acts through the beam equation. We prove using the same technique as for the first model combined with some interpolation inequalities and by solving ordinary differential equations of order 4, that the energy has a polynomial decay rate of type t^{frac{−2}{ 2−α}} . Finally, in the third model, we consider an Euler-Bernoulli beam with a localized non-regular fractional Kelvin-Voigt damping. We show that the energy has a polynomial decay rate of type t^{frac{−2}{1−α}} , where α ∈ (0,1).