  We propose a local discontinuous Galerkin (LDG) method for fractional
Korteweg-de Vries equation involving the fractional Laplacian with exponent
$\alpha\in (1,2)$ in one and two space dimensions. By decomposing the
fractional Laplacian into a first order derivative and a fractional integral,
we prove $L^2$-stability of the semi-discrete LDG scheme incorporating suitable
interface and boundary fluxes. We analyze the error estimate by considering
linear convection term and utilizing the estimate, we derive the error estimate
for general nonlinear flux and demonstrate an order of convergence
$\mathcal{O}(h^{k+1/2})$. Moreover, the stability and error analysis have been
extended to multiple space dimensional case. Numerical illustrations are shown
to demonstrate the efficiency of the scheme by obtaining an optimal order of
convergence.
