  We study a reaction diffusion system where we consider a non-gaussian process
instead of a standard diffusion. If the process increments follow a probability
distribution with tails approaching to zero faster than a power law, the usual
qualitative behaviours of the standard reaction diffusion system, i.e.,
exponential tails for the reacting field and a constant front speed, are
recovered. On the contrary if the process has power law tails, also the
reacting field shows power law tail and the front speed increases exponentially
with time. The comparison with other reaction-transport systems which exhibit
anomalous diffusion shows that, not only the presence of anomalous diffusion,
but also the detailed mechanism, is relevant for the front propagation.
