  We consider a pseudo-differential equation driven by the fractional
$p$-Laplacian with $p\ge 2$ (degenerate case), with a bounded reaction $f$ and
Dirichlet type conditions in a smooth domain $\Omega$. By means of barriers, a
nonlocal superposition principle, and the comparison principle, we prove that
any weak solution $u$ of such equation exhibits a weighted H\"older regularity
up to the boundary, that is, $u/d^s\in C^\alpha(\overline\Omega)$ for some
$\alpha\in(0,1)$, $d$ being the distance from the boundary.
