  Decoupled fractional Laplacian wave equation can describe the seismic wave
propagation in attenuating media. Fourier pseudospectral implementations, which
solve the equation in spatial frequency domain, are the only existing methods
for solving the equation. For the earth media with curved boundaries, the
pseudospectral methods could be less attractive to handle the irregular
computational domains. In the paper, we propose a radial basis function
collocation method that can easily tackle the irregular domain problems. Unlike
the pseudospectral methods, the proposed method solves the equation in physical
variable domain. The directional fractional Laplacian is chosen from varied
definitions of fractional Laplacian. Particularly, the vector
Gr\"unwald-Letnikov formula is employed to approximate fractional directional
derivative of radial basis function. The convergence and stability of the
method are numerically investigated by using the synthetic solution and the
long-time simulations, respectively. The method's flexibility is studied by
considering homogeneous and multi-layer media having regular and irregular
geometric boundaries.
