  In this work, we consider a system of multidimensional wave equations coupled
by velocities with one localized fractional boundary damping. First, using a
general criteria of Arendt- Batty, by assuming that the boundary control region
satisfy some geometric conditions, under the equality speed propagation and the
coupling parameter of the two equations is small enough, we show the strong
stability of our system in the absence of the compactness of the resolvent. Our
system is not uniformly stable in general since it is the case of the interval.
Hence, we look for a polynomial decay rate for smooth initial data for our
system by applying a frequency domain approach combining with a multiplier
method. Indeed, by assuming that the boundary control region satisfy some
geometric conditions and the waves propagate with equal speed and the coupling
parameter term is small enough, we establish a polynomial energy decay rate for
smooth solutions, which depends on the order of the fractional derivative.
