In this talk, we deal with the fine boundary regularity, a weighted H\{o}lder regularity of weak solutions to the problem involving the fractional $(p,q)$-Laplacian denoted by
$(-\Delta)_{p}^{s} u + (-\Delta)_{q}^{s} u = f(x)$ in $\Omega,$
and $u=0$ in $\mathbb{R}^N\setminus\Omega;$
where $\Omega$ is a $C^{1,1}$ bounded domain and $2 \leq p \leq q