  By virtue of barrier arguments we prove $C^\alpha$-regularity up to the
boundary for the weak solutions of a non-local nonlinear problem driven by the
fractional $p$-Laplacian operator. The equation is boundedly inhomogeneous and
the boundary conditions are of Dirichlet type. We employ different methods
according to the singular ($p<2$) of degenerate ($p>2$) case.
