Energy estimates for two-dimensional space-Riesz fractional wave equation

The fractional wave equation governs the propagation of mechanical diffusive waves in viscoelastic media which exhibits a power-law creep, and consequently provided a physical interpretation of this equation in the framework of dynamic viscoelasticity. In this paper, we first use the energy method to estimate the one-dimensional space-Riesz fractional wave equation. The stiff matrices are proved to be commutative for two-dimensional case, which ensures to carry out of the priori error estimates and the energy method. Then, the unconditional stability and convergence with the global truncation error O ( τ 2 + h 2 ) are theoretically proved with the constant coefficients and numerically verified.