  \noi We study the following nonlinear system with perturbations involving
p-fractional Laplacian \begin{equation*} (P)\left\{ \begin{split} (-\De)^s_p u+
a_1(x)u|u|^{p-2} &= \alpha(|x|^{-\mu}*|u|^q)|u|^{q-2}u+ \beta
(|x|^{-\mu}*|v|^q)|u|^{q-2}u+ f_1(x)\; \text{in}\; \mb R^n,\\ (-\De)^s_p v+
a_2(x)v|v|^{p-2} &= \gamma(|x|^{-\mu}*|v|^q)|v|^{q-2}v+ \beta
(|x|^{-\mu}*|u|^q)|v|^{q-2}v+ f_2(x)\; \text{in}\; \mb R^n, \end{split} \right.
\end{equation*} where $n>sp$, $0<s<1$, $p\geq2$, $\mu \in (0,n)$,
$\frac{p}{2}\left( 2-\frac{\mu}{n}\right) < q <\frac{p^*_s}{2}\left(
2-\frac{\mu}{n}\right)$, $\alpha,\beta,\gamma >0$, $0< a_i \in C^1(\mb R^n, \mb
R)$, $i=1,2$ and $f_1,f_2: \mb R^n \to \mb R$ are perturbations. We show
existence of atleast two nontrivial solutions for $(P)$ using Nehari manifold
and minimax methods.
