We study the following nonlinear system with perturbations involving⎧p-fractional Laplacian: (Formula Presented) where n > sp, 0 < s < 1, p ≥ 2, µ ∈ (0, n), p(2 − µ/n)/2 < q < p∗ s(2 − µ/n)/2, α, β, γ > 0, 0 < ai ∈ C(Rn, R), i = 1, 2 and f1, f2: Rn → R are perturbations. We show existence of at least two nontrivial solutions for (P) using Nehari manifold and minimax methods. © 2018 Juliusz Shauder Centre for Nonlinear Studies Niolaus Copernius University.