Asymptotic behavior of a fractional Fokker–Planck-type equation

Abstract

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 〈 ( Δ x ) 2 ( t ) 〉 ∼ t γ and 〈 ( Δ x ) 2 ( t ) 〉 ∼ x - θ t γ ( 0 < γ < 1 ,- ∞ < θ < + ∞ ) , respectively.