  We study the reaction-fractional-diffusion equation $u_t+(-\Delta)^{s}
u=f(u)$ with ignition and monostable reactions $f$, and $s\in(0,1)$. We obtain
the first optimal bounds on the propagation of front-like solutions in the
cases where no traveling fronts exist. Our results cover most of these cases,
and also apply to propagation from localized initial data.
