Answer to an open problem proposed by R Metzler and J Klafter

摘要

In a positive answer to the open problem proposed by R Metzler and J Klafter, it is proved that the asymptotic shape of the solution for a wide class of fractional Fokker-Planck equations is a stretched Gaussian for the initial condition being a pulse function in the homogeneous and heterogeneous fractal structures, whose mean square displacement behaves like <(Delta x)(2)(t)>similar to t(V) and <(Delta x)(2)(t)>similar to x(-theta)t(V)(0 < gamma < 1, -infinity < theta < +infinity), respectively.