  We study the existence of solutions to the fractional elliptic equation (E1)
$(-\Delta)^\alpha u+\epsilon g(|\nabla u|)=\nu $ in a bounded regular domain
$\Omega$ of $\R^N (N\ge2)$, subject to the condition (E2) $u=0$ in $\Omega^c$,
where $\epsilon=1$ or $-1$, $(-\Delta)^\alpha$ denotes the fractional Laplacian
with $\alpha\in(1/2,1)$, $\nu$ is a Radon measure and $g:\R_+\mapsto\R_+$ is a
continuous function. We prove the existence of weak solutions for problem
(E1)-(E2) when $g$ is subcritical. Furthermore, the asymptotic behavior and
uniqueness of solutions are described when $\nu$ is Dirac mass, $g(s)=s^p$,
$p\geq 1$ and $\epsilon=1$.
