  In this work we study the existence of positive solution to the fractional
quasilinear problem, $$ \left\{ \begin{array}{rcll} (-\Delta )^s u &=&\lambda
\dfrac{u}{|x|^{2s}}+ |\nabla u|^{p}+ \mu f &\inn \Omega,\\ u&>&0 &
\inn\Omega,\\ u&=&0 & \inn(\mathbb{R}^N\setminus\Omega), \end{array}\right. $$
where $\Omega$ is a $C^{1,1}$ bounded domain in $\mathbb{R}^N$, $N> 2s, \mu>0$,
$\frac{1}{2}<s<1$, and $0<\lambda<\Lambda_{N,s}$ is defined in (3) . We assume
that $f$ is a non-negative function with additional hypotheses.
  As we will see, there are deep differences with respect to the case
$\lambda=0$. More precisely, If $\lambda>0$, there exists a critical exponent
$p_{+}(\lambda, s)$ such that for $p> p_{+}(\lambda,s)$ there is no positive
solution. Moreover, $p_{+}(\lambda,s)$ is optimal in the sense that, if
$p<p_{+}(\lambda,s)$ there exists a positive solution for suitable data and
$\mu$ sufficiently small.
