  In this article, we deal with the existence of non-negative solutions of the
class of following non local problem $$ \left\{ \begin{array}{lr}
  \quad - M\left(\displaystyle\int_{\mathbb R^n}\int_{\mathbb R^{n}}
\frac{|u(x)-u(y)|^{\frac{n}{s}}}{|x-y|^{2n}}~dxdy\right) (-\Delta)^{s}_{n/s}
u=\left(\displaystyle\int_{\Omega}\frac{G(y,u)}{|x-y|^{\mu}}~dy\right)g(x,u) \;
\text{in}\; \Omega,\\ \quad \quad u =0\quad\text{in} \quad \mathbb R^n
\setminus \Omega, \end{array} \right. $$ where $(-\Delta)^{s}_{n/s}$ is the
$n/s$-fractional Laplace operator, $n\geq 1$, $s\in(0,1)$ such that $n/s\geq
2$, $\Omega\subset \mathbb R^n$ is a bounded domain with Lipschitz boundary,
$M:\mathbb R^+\rightarrow \mathbb R^+$ and $g:\Omega\times\mathbb R\rightarrow
\mathbb R$ are continuous functions, where $g$ behaves like
$\exp({|u|^{\frac{n}{n-s}}})$ as $|u|\rightarrow\infty$.
