  In this paper, we investigate the existence of weak solution for a Kirchhoff
type problem driven by a nonlocal operator of elliptic type in a fractional
Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions
  {\small$$
  (D_{K,A}) \hspace*{0.5cm} \left\{
  \begin{array}{clclc}
  M\left( \displaystyle \int_{\R^{2N}}A\left( [u(x)-u(y)] K(x,y)\right)
dxdy\right) \mathcal{L}^K_A u & = & f(x,u) & \text{ in }& \Omega,
  \hspace*{7cm} u & = & 0 \hspace*{0.2cm} \hspace*{0.2cm} & \text{ in } &
\R^N\setminus \Omega.
  \label{eq1}
  \end{array}
  \right. $$ } Where $\mathcal{L}^K_A$ is a nonlocal operator with singular
kernel $K$ and $A$ is an $N$-function, $\Omega$ is an open bounded subset in
$\R^N$ with Lipschitz boundary $\partial \Omega$.
