LAUSR

This paper considers a class of fractional Schrodinger–Poisson type systems with doubly critical growth $$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^su+V(x)u-\phi |u|^{2^*_s-3}u=K(x)|u|^{2^*_s-2}u,&{} \text{ in } {\mathbb {R}}^3,\\ (-\Delta )^s\phi =|u|^{2^*_s-1},&{} \text{ in } {\mathbb {R}}^3, \end{array}\right. \end{aligned}$$ where $$s\in (3/4,1)$$ , $$2^*_s=\frac{6}{3-2s}$$ , $$V\in L^{\frac{3}{2s}}({\mathbb {R}}^{3})$$ , $$K\in L^{\infty }({\mathbb {R}}^{3})$$ . By applying the concentration-compactness principle and variational method, the existence of ground state solutions to the systems is derived.