  We determine the wave front sets of solutions to two special cases of the
Cauchy problem for the space-time fractional Zener wave equation, one being
fractional in space, the other being fractional in time. For the case of the
space fractional wave equation, we show that no spatial propagation of
singularities occurs. For the time fractional Zener wave equation, we show an
analogue of non-characteristic regularity.
