Convergence analysis of a fully discrete scheme for diffusion-wave equation forced by tempered fractional Brownian motion

In this paper, we investigate a fully discrete approximation of stochastic diffusion-wave equation driven by additive tempered fractional Gaussian noise. This additive noise exhibits semi-long range dependence. The model involves two nonlocal terms in time, i.e., a Caputo fractional derivative and a tempered fractional Brownian motion. The space discretization is achieved via the spectral Galerkin method. The Caputo fractional derivative of order alpha is an element of(1, 2) is approximated by using the Grunwald-Letnikov formula. Combining Mittag-Leffler function, Laplace transform and z-transform, we establish the error estimates of the full discretization in the sense of mean-squared L-2- norm. Numerical experiments are presented to confirm the strong convergence rates.