  We study a rough differential equation driven by fractional Brownian motion
with Hurst parameter $H$ $(1/4<H \le 1/2)$. Under H\"ormander's condition on
the coefficient vector fields, the solution has a smooth density for each fixed
time. Using Watanabe's distributional Malliavin calculus, we obtain a short
time full asymptotic expansion of the density under quite natural assumptions.
Our main result can be regarded as a "fractional version" of Ben Arous' famous
work on the off-diagonal asymptotics.
