Fractional Laplacian system involving doubly critical nonlinearities in $\mathbb{R}^N

In this article, we are interested in a fractional Laplacian system in $\mathbb{R}^N$, which involves critical Sobolev-type nonlinearities and critical Hardy–Sobolev-type nonlinearities. By using variational methods, we investigate the extremals of the corresponding best fractional Hardy–Sobolev constant and establish the existence of solutions. To our best knowledge, our main results are new in the study of the fractional Laplacian system.