  We study the Cauchy problem for the fractional Schr\"{o}dinger equation $$
i\partial_tu = (m^2-\Delta)^\frac\alpha2 u + F(u) in \mathbb{R}^{1+n}, $$ where
$ n \ge 1$, $m \ge 0$, $1 < \alpha < 2$, and $F$ stands for the nonlinearity of
Hartree type: $$F(u) = \lambda (\frac{\psi(\cdot)}{|\cdot|^\gamma} * |u|^2)u$$
with $\lambda = \pm1, 0 <\gamma < n$, and $0 \le \psi \in L^\infty(\mathbb
R^n)$. We prove the existence and uniqueness of local and global solutions for
certain $\alpha$, $\gamma$, $\lambda$, $\psi$. We also remark on finite time
blowup of solutions when $\lambda = -1$.
