Asymptotic behavior of Fokker-Planck-type a fractional equation

作者:Ren Fu Yao*; Liang Jin Rong; Qiu Wei Yuan; Xiao Han Bin
来源:Physica A: Statistical Mechanics and Its Applications , 2007, 373: 165-173.
DOI:10.1016/j.physa.2006.05.045

摘要

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 <(Delta X)(2) (t)>similar to t(gamma) and <(Delta x)(2)(t)>similar to x(-theta)t(gamma) (0 <gamma < 1, -infinity <theta <+infinity), respectively.