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

Energy Decay of some boundary coupled systems involving wave$\backslash$  Euler-Bernoulli beam with one locally singular fractional Kelvin-Voigt  damping