Abstract In the paper, we study the higher regularity and decay estimates for positive solutions of the following fractional Choquard equations: 0.1 (−Δ)su+λu=(Iα∗|u|p)|u|p−2uinRN,lim|x|→∞u(x)=0,u∈Hs(RN),$$\begin{equation} {\left\lbrace \begin{aligned} &(-\Delta)^s u+\lambda u=(I_\alpha *|u|^p)|u|^{p-2}u\quad \mathrm{in}\ \mathbb {R}^N,\\ &\lim _{|x|\rightarrow \infty }u(x)=0,\quad u\in H^s(\mathbb {R}^N), \end{aligned}\right.} \end{equation}$$where Iα=1|x|N−α$I_\alpha =\frac{1}{|x|^{N-\alpha }}$, λ>0$\lambda >0$ is a constant, ...
