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In this work, we consider a system of multidimensional wave equations coupledby velocities with one localized fractional boundary damping. First, using ageneral criteria of Arendt- Batty, by assuming that the boundary control regionsatisfy some geometric conditions, under the equality speed propagation and thecoupling parameter of the two equations is small enough, we show the strongstability of our system in the absence of the compactness of the resolvent. Oursystem 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 oursystem by applying a frequency domain approach combining with a multipliermethod. Indeed, by assuming that the boundary control region satisfy somegeometric conditions and the waves propagate with equal speed and the couplingparameter term is small enough, we establish a polynomial energy decay rate forsmooth solutions, which depends on the order of the fractional derivative.

Indirect stability of a multidimensional coupled wave equations with one locally boundary fractional damping