Exact solution with existence and uniqueness conditions for multi-dimensional time-space tempered fractional diffusion-wave equation

Abstract

In this paper, we investigate the existence and uniqueness of the multi-dimensional time-space tempered fractional diffusion-wave (TSTFDW) equation by using the fixed point theory. We also found an exact solution of the multi-dimensional TSTFDW equation. The two-step Adomian decomposition method is proposed to achieve the exact solution of this problem. The main advantages of this method are its easy implementation and higher efficiency than other existing numerical methods.