We develop an iterative approach, from which an exact systematic calcu
lation of the moments of the probability density of test particles, un
der a generalized Fickian evolution and in the presence of a stratifie
d random velocity field, can be calculated. The type of fractional dif
fusion-advection equation studied is useful for transport in anisotrop
ic and heterogeneous media, Our method stresses the relevance of the c
oupling between anomalous diffusion and convection by stratified rando
m velocity fields. [S0031-9007(98)07342-6].