- - - Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
- - - Department of Mathematics, Faculty of Basisc Sciences, Babol(Noshirvani) University of Technology Babol, Iran
- - - Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

In this paper, we are concerned with the following fractional Schrödinger-Poisson system:  \left\{                                   \begin{array}{ll}                                    (-\Delta^s)u+u+\lambda\phi u=\mu f(n)+|u|^{p-۲}|u|, & x\in\mathbb{R}^۳ \\                                     (-\Delta^t)\phi=u^۲, & x\in\mathbb{R}^۳                                   \end{array}                                 \right. where \lambda,\mu are two parameters, s,t \in (۰,۱], ۲t + ۴s > ۳ ,۱ < p ≤ ۲_s^∗ and f : \mathbb{R} \longrightarrow \mathbb{R} is continuous function. Using some critical point theorems and truncation technique, we obtain the existence and multiplicity of non-trivial solutions with the help of the vibrational methods.

Fractional Schrödinger-Poisson systems, Sublinear nonlinearity, Variational methods