Lévy Processes Linked to the Lower-Incomplete Gamma Function

We start by defining a subordinator means of the lower-incomplete gamma function. This can be considered as an approximation stable subordinator, easier to handled in view its finite activity. A tempered version is also order overcome drawback infinite moments. Then, we study Lévy processes that are time-changed these subordinators with particular attention Brownian case. An fractional derivative (as well power operators) arises from analysis governing equations. Finally, show time-changing motion produces model anomalous diffusion, which exhibits sub-diffusive behavior.