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The present study is concerned with the following fractionalSchr\"{o}dinger-Poisson system with steep potential well: $$  \left\{% \begin{array}{ll}  (-\Delta)^s u+ \la V(x)u+K(x)\phi u= f(u), & x\in\R^3,  (-\Delta)^t \phi=K(x)u^2, & x\in\R^3, \end{array}% \right. $$ where$s,t\in(0,1)$ with $4s+2t>3$, and $\la>0$ is a parameter. Under certainassumptions on $V(x)$, $K(x)$ and $f(u)$ behaving like $|u|^{q-2}u$ with$2<q<2_s^*=\frac{6}{3-2s}$, the existence of positive ground state solutionsand concentration results are obtained via some new analytical skills andNehair-Poho\v{z}aev identity. In particular, the monotonicity assumption on thenonlinearity is not necessary.

The existence and concentration of positive ground state solutions for a  class of fractional Schr\"{o}dinger-Poisson systems with steep potential  wells