  The traditional wave equation models wave propagation in an ideal conducting
medium. For characterizing the wave propagation in inhomogeneous media with
frequency dependent power-law attenuation, the space-time fractional wave
equation appears; further incorporating the additive white Gaussian noise
coming from many natural sources leads to the stochastic space-time fractional
wave equation. This paper discusses the Galerkin finite element approximations
for the stochastic space-time fractional wave equation forced by an additive
space-time white noise. We firstly discretize the space-time additive noise,
which introduces a modeling error and results in a regularized stochastic
space-time fractional wave equation; then the regularity of the regularized
equation is analyzed. For the discretization in space, the finite element
approximation is used and the definition of the discrete fractional Laplacian
is introduced. We derive the mean-squared $L^2$-norm priori estimates for the
modeling error and for the approximation error to the solution of the
regularized problem; and the numerical experiments are performed to confirm the
estimates. For the time-stepping, we calculate the analytically obtained
Mittag-Leffler type function.

Numerical Analysis