  In this paper we define the fractional order Orlicz-Sobolev spaces, and prove
its convergence to the classical Orlicz-Sobolev spaces when the fractional
parameter $s\uparrow 1$ in the spirit of the celebrated result of
Bourgain-Brezis-Mironescu. We then deduce some consequences such as
$\Gamma-$convergence of the modulars and convergence of solutions for some
fractional versions of the $\Delta_g$ operator as the fractional parameter
$s\uparrow 1$.
