  For $s\textgreater{}0$, let $H\_0=(-\Delta)^s$ be the fractional Laplacian.
In this paper, we obtainLieb-Thirring type inequalities for the fractional
Schr\"odinger operator defined as $H=H\_0+V$,where $V \in L^p(\mathbb{R}^d),
p\ge 1, d\ge 1,$ is a complex-valued potential.Our methods are based on results
of articles by Borichev-Golinskii-Kupin \cite{BoGoKu} and Hansmann \cite{Ha1}.
