Universality of stretched Gaussian asymptotic diffusion behavior on biased heterogeneous fractal structure in external force fields

A biased heterogeneous fractional Fokker–Planck equation (BHFFPE) is introduced to model the anomalous diffusion on biased heterogeneous fractal structure media describing systems involving external force fields. It is shown that the BHFFPE obeys the generalized Einstein relation, and that the asymptotic shape of its solution is a stretched Gaussian. The theoretic results obtained is consistent with GER.