  Partial differential equations (p.d.e) equipped of spatial derivatives of
fractional order capture anomalous transport behaviors observed in diverse
fields of Science. A number of numerical methods approximate their solutions in
dimension one. Focusing our effort on such p.d.e. in higher dimension with
Dirichlet boundary conditions, we present an approximation based on Lattice
Boltzmann Method with Bhatnagar-Gross-Krook (BGK) or Multiple-Relaxation-Time
(MRT) collision operators. First, an equilibrium distribution function is
defined for simulating space-fractional diffusion equations in dimensions 2 and
3. Then, we check the accuracy of the solutions by comparing with i) random
walks derived from stable L\'evy motion, and ii) exact solutions. Because of
its additional freedom degrees, the MRT collision operator provides accurate
approximations to space-fractional advection-diffusion equations, even in the
cases which the BGK fails to represent because of anisotropic diffusion tensor
or of flow rate destabilizing the BGK LBM scheme.
