  In this paper, we investigate the energy decay of hyperbolic systems of
wave-wave, wave-Euler- Bernoulli beam and beam-beam types. The two equations
are coupled through boundary connection with only one localized non-smooth
fractional Kelvin-Voigt damping. First, we reformulate each system into an
augmented model and using a general criteria of Arendt-Batty, we prove that our
models are strongly stable. Next, by using frequency domain approach, combined
with multiplier technique and some interpolation inequalities, we establish
different types of polynomial energy decay rate which depends on the order of
the fractional derivative and the type of the damped equation in the system.
