Asymptotic behavior of a fractional Fokker–Planck-type equation

It is proved that the asymptotic shape of the solution for a wide class of fractional Fokker–Planck-type equations with coefficients depending on coordinate and time is a stretched Gaussian for the initial condition being pulse function in the homogeneous and heterogeneous fractal structures, whose mean square displacement behaves like 〈(Δx)2(t)〉∼tγ〈(Δx)2(t)〉∼tγ and 〈(Δx)2(t)〉∼x-θtγ(0<γ<1,-∞<θ<+∞), respectively.