  In this paper, we provide a framework of designing the local discontinuous
Galerkin scheme for integral fractional Laplacian $(-\Delta)^{s}$ with
$s\in(0,1)$ in two dimensions. We theoretically prove and numerically verify
the numerical stability and convergence of the scheme with the convergence rate
no worse than $\mathcal{O}(h^{k+\frac{1}{2}})$.
