(-Δ)^p stands for the fractional Laplacian, ω > 0 is a constant, V is vanishing potential and K is a smooth function. Under some suitable conditions on K and f, we obtain a Palais-Smale sequence by using a weaker Ambrosetti-Rabinowitz condition and prove the ground state solution for this system by employing variational methods. In particular, this kind of problem is a vast range of applications and challenges.