Abstract
In this paper, we study the existence of multiple solutions to some sub-critical and critical systems involving the fractional p-Laplacian operator. Our main tools are based on variational methods. Precisely, the Nehari manifold method combined with fibering map are used in the study of the sub-critical case. While in the critical one, we use the mountain pass theorem combined with Nehari manifold and Brezis-Lieb lemma.