  Granular material flowing on complex topographies are ubiquitous in
industrial and geophysical situations. In this paper, we study the small-scale
model of a granular layer flowing on a rough incline. The shape of a granular
front is solved analytically by using a 1D Savage-Hutter's model based on
depth-averaged mass and momentum equations with the fractional expression for
the frictional rheology $\mu(I)$. Unlike previous studies where a "plug flow"
is assumed, a free shape factor $\alpha$ describing the vertical velocity
profile, is taken into account to determine the solution. Such a way, we put in
evidence an effect of inertia through the Froude number Fr and the shape factor
$\alpha$ on the front profile. The analytical predictions are compared with
experimental results published by [O. Pouliquen, Phys. Fluids 11, 1956 (1999)]
and with our new experimental data obtained at higher Froude numbers. A good
agreement between theory and experiments is found when $\alpha$ = 5/4 is used
in our model, corresponding to a Bagnold-like velocity profile. However, open
questions are raised about the vertical velocity profile in granular flows and
about the expression of the rheological function $\mu(I)$ and its calibration
from experimental data.
