  In this paper, we investigate the numerical solution of the two-dimensional
fractional Laplacian wave equations. After splitting out the Riesz fractional
derivatives from the fractional Laplacian, we treat the Riesz fractional
derivatives with an implicit scheme while solving the rest part explicitly.
Thanks to the tensor structure of the Riesz fractional derivatives, a splitting
alternative direction implicit (S-ADI) scheme is proposed by incorporating an
ADI remainder. Then the Gohberg-Semencul formula, combined with fast Fourier
transform, is proposed to solve the derived Toeplitz linear systems at each
time integration. Theoretically, we demonstrate that the S-ADI scheme is
unconditionally stable and possesses second-order accuracy. Finally, numerical
experiments are performed to demonstrate the accuracy and efficiency of the
S-ADI scheme.
