Relaxation to stationary states for anomalous diffusion

The fractional Fokker–Planck–Smoluchowski equation serves as a standard description of the anomalous diffusion. Within a current presentation we study properties of stationary states of the fractional Fokker–Planck–Smoluchowski equation in bounding potentials with special attention to the way in which stationary states are approached. It is demonstrated that the shape of the stationary state depends on exponents characterizing the jump length distributions and the external potential. The convergence rate to the stationary state can be of the double power-law type and is determined solely by the subdiffusion parameter.

► We study properties of stationary states of the fractional Fokker–Planck equation in bounding potentials with special attention to the way in which stationary states are approached.
► It is demonstrated that the shape of the stationary state depends on the exponent characterizing the jump length distributions and the external potential.
► The convergence rate to the stationary state can be of the double power-law type and is determined solely by the subdiffusion parameter.