Coupled continuous time random walk with Lévy distribution jump anomalous diffusion?

The continuous time random walk (CTRW) models are highly valued for studying anomalous diffusion, a ubiquitous phenomenon in complex media whose mean squared displacement (MSD) exhibits power-law behavior. It is widely accepted that the Levy distribution jump length random particles with infinite second moment could be responsible for the superdiffusion phenomenon. In this paper, we study the coupled CTRW with exponentially truncated Levy distribution jump length, deduce the corresponding integrodifferential diffusion equation, and give propagator expression. It is interesting that we find the MSD for random particles is linearly related to time in the symmetric Levy distribution case, and it reduces to a simple expression. Additionally, for a non-zero truncated exponent, the MSD also has a linear relationship with time, which reflects the special dependence between waiting time and jump length in this coupled CTRW model.