Fokker–Planck type equations associated with fractional Brownian motion controlled by infinitely divisible processes

In this paper we study the anomalous diffusion process driven by fractional Brownian motion delayed by general infinitely divisible subordinator. We show the analyzed process is the stochastic representation of the Fokker–Planck type equation that describes the probability density function of an introduced model. Moreover, we study main characteristics of the examined process, the first two moments, that allow us in special cases for classification of it as a system with accelerating-subdiffusion property.