  Let $f: X \rightarrow Z$ be a fibration from a normal projective variety $X$
of dimension $n$ onto a normal curve $Z$ over a perfect field of characteristic
$p>2$. Let $(X, B)$ be a log canonical pair such that the induced pair on the
general fibre is log canonical. Assuming the LMMP and the existence of log
resolutions in dimension $\leq n$, we prove that, up to a birational map $Y
\dashrightarrow X$, the moduli part is nef. As a corollary, we prove nefness of
the moduli part in the $f$-trivial case, i.e. when $K_X+B \sim_{\mathbb{Q}}
f^*L$ for some $\mathbb{Q}$-Cartier $\mathbb{Q}$-divisor $L$ on $Z$. In
particular, consider a log canonical pair $(X, B)$ of dimension 3 over a
perfect field of characteristic $p>5$ such that the induced pair on the general
fibre is log canonical. Then, we conclude that the canonical bundle formula
holds.
