  SSC emission from a reverse shock has been suggested as the origin for the
high energy component lasting 2 s in the prompt phase of GRB98080923 (Fraija et
al. 2012). The model describes spectral indices, fluxes and the duration of the
high-energy component as well as a long keV tail present in the prompt phase of
GRB980923. Here, we present an extension of this model to describe the
high-energy emission of GRB090926A. We argue that the emission consist of two
components, one with a duration less than 1s during the prompt phase, and a
second, longer-lasting GeV phase lasting hundred of seconds after the prompt
phase. The short high-energy phase can be described as SSC emission from a
reverse shock similar to that observed in GRB980923, while the longer component
arises from the forward shock. The main assumption is that the jet is
magnetized and evolves in the thick-shell case, and the calculated fluxes and
break energies are all consistent with the observed values. A comparison
between the resulting parameters obtained for GRB980923 and GRB090926A suggests
differences in burst tails that could be attributable to the circumburst
medium, and this could account for previous analyses reported in the literature
for other bursts. We find that the density of the surrounding medium inferred
from the observed values associated to the forward shock agrees with standard
values for host galaxies such as the one associated to GRB090926A.
