  We establish upper bounds for the decay rate of the energy of the damped
fractional wave equation when the averages of the damping coefficient on all
intervals of a fixed length are bounded below. If the power of the fractional
Laplacian, $s$, is between 0 and 2, the decay is polynomial. For $s \ge 2$, the
decay is exponential. Second, we show that our assumption on the damping is
necessary for the energy to decay exponentially.
