Fractional elliptic equations with Hardy potential and critical nonlinearities

In this paper, we consider the fractional elliptic equation \begin{align*} \left{\begin{aligned} &(-\Delta)^s u-\mu\frac{u}{|x|^{2s}} = \frac{|u|^{2_s^\ast (\alpha)-2}u}{|x|^{\alpha}} + f(x,u), && \mbox{in}
\Omega,\ &u=0, && \mbox{in} \ $\mathbb{R}$^{n}\backslash \ \Omega, \end{aligned}\right. \end{align*} where $\mathrm{\Omega }\subset R^n$ is a smooth bounded domain, $0\in \mathrm{\Omega }$, $0<s<1$, $0<\alpha <2s<n$, $2_s^{\ast }(\alpha )=\frac{2(n-\alpha )}{n-2s}$. Under some assumptions on $\mu$ and $f$, we obtain the existence of nonnegative solutions.