We study the boundary weighted regularity of weak solutions $u$ to a $s$-fractional $p$-Laplacian equation in a bounded smooth domain $Ω$ with bounded reaction and nonlocal Dirichlet type boundary condition, in the singular case $p\in(1,2)$ and with $s\in(0,1)$. We prove that $u/{\rm d}_Ω^s$ has a $α$-Hölder continuous extension to the closure of $Ω$, ${\rm d}_Ω(x)$ meaning the distance of $x$ from the complement of $Ω$. This result corresponds to that of ref. [28] for the degenerate case $p\ge 2$.

47 pages, 2 figures