In this paper, we study the existence result for a class of fractional Schrödinger-Possion system. Using variational method and Nehari method, we obtianed a uniqueness result for positive solutions.

This paper is devoted to the following fractional Schrödinger-Poisson systems: \begin{equation*} \left\{\aligned &(-\Delta)^{s} u+V(x)u+\phi(x)u= f(x,u) \,\,\,&\text{in } \mathbb{R}^3, \\ & (-\Delta)^{t} \phi(x)=u^2 \,\,\,&\text{in } \mathbb{R}^3, \endaligned \right. \end{equation*} where $(-\Delta)^{s}$ is the fractional Lapalcian, $s, t \in (0, 1),$ $V : \R^3 \to \R$ is continuous. In contrast to most studies, we consider that the potentials $V$ is indefinite. With the help of Morse theory, the existence of nontrivial solutions for the above problem is obtained.