On dynamical behaviors in the fractional generalized Langevin equation

The focus of our study in this paper is on the active dynamics and a fractional generalized Langevin equation with a memory kernel K(t). The Fokker-Planck equation is obtained by deriving it from a second-order differential equation. The joint probability density we obtained enables us to calculate various statistical quantities such as mean squared displacement and mean squared velocity in different three-time domains.