  In this article, our main concern is to study the existence of bound and
ground state solutions for the following fractional system of nonlinear
Schr\"odinger-Korteweg-De Vries (NLS-KdV, in short) equations with Hardy
potentials:
  \begin{equation*}
  \left\{
  \begin{aligned}
  (-\Delta)^{s_{1}} u - \lambda_{1} \frac{u}{|x|^{2s_{1}}} -
u^{2_{s_{1}}^{*}-1} &= 2\nu h(x) u^{}v^{} & \quad \mbox{in} ~ \mathbb{R}^{N},
  (-\Delta)^{s_{2}} v - \lambda_{2} \frac{v}{|x|^{2s_{2}}} -
v^{2_{s_{2}}^{*}-1} &= \nu h(x) u^{2} & \quad \mbox{in} ~ \mathbb{R}^{N},
  u,v >0 \quad \mbox{in} ~ \mathbb{R}^{N} \setminus \{0\},
  \end{aligned}
  \right. \end{equation*}
  where $s_{1},s_{2} \in (0,1)~\text{and}~\lambda_{i}\in (0,
\Lambda_{N,s_{i}})$ with $\Lambda_{N,s_{i}} = 2 \pi^{N/2}
\frac{\Gamma^{2}(\frac{N+2s_i}{4})
\Gamma(\frac{N+2s_i}{2})}{\Gamma^{2}(\frac{N-2s_i}{4}) ~|\Gamma(-s_{i})|},
(i=1,2)$. By imposing certain assumptions on the parameter $\nu$ and on the
function $h$, we obtain ground-state solutions using the
concentration-compactness principle and the mountain-pass theorem.
