  In this paper we consider a system of two reaction-diffusion equations that
models diffusional-thermal combustion with stepwise ignition-temperature
kinetics and fractional reaction order 0 < $\alpha$ < 1. We turn the free
interface problem into a scalar free boundary problem coupled with an integral
equation. The main intermediary step is to reduce the scalar problem to the
study of a non-C 1 vector field in dimension 2. The latter is treated by
qualitative topo-logical methods based on the Poincar{\'e}-Bendixson Theorem.
The phase portrait is determined and the existence of a stable manifold at the
origin is proved. A significant result is that the settling time to reach the
origin is finite, meaning that the trailing interface is finite in contrast to
the case $\alpha$ = 1, but in accordance with $\alpha$ = 0. Finally, the
integro-differential system is solved via a fixed-point method.
