From the Langevin equation to the fractional Fokker–Planck equation

It is demonstrated how the competition of Langevin-type motion driven by a δ-correlated, Gaussian noise with a trapping mechanism results in a fractional generalisation of the Klein-Kramers equation. From the latter, the fractional Fokker-Planck equation is derived which describes subdiffusion processes in an external force field. A solution for the subdiffusive Ornstein-Uhlenbeck process is presented.