  The fractional Laplacian has been strongly studied during past decades. In
this paper we present a different approach for the associated Dirichlet
problem, using recent deep learning techniques. In fact, intensively PDEs with
a stochastic representation have been understood via neural networks,
overcoming the so-called curse of dimensionality. Among these equations one can
find parabolic ones in $\mathbb{R}^d$ and elliptic in a bounded domain $D
\subset \mathbb{R}^d$. In this paper we consider the Dirichlet problem for the
fractional Laplacian with exponent $\alpha \in (1,2)$. We show that its
solution, represented in a stochastic fashion can be approximated using deep
neural networks. We also check that this approximation does not suffer from the
curse of dimensionality.
