  The problem of diffusion in a time-dependent (and generally inhomogeneous)
external field is considered on the basis of a generalized master equation with
two times, introduced in [1,2]. We consider the case of the quasi Fokker-Planck
approximation, when the probability transition function for diffusion
(PTD-function) does not possess a long tail in coordinate space and can be
expanded as a function of instantaneous displacements. The more complicated
case of long tails in the PTD will be discussed separately. We also discuss
diffusion on the basis of hydrodynamic and kinetic equations and show the
validity of the phenomenological approach. A new type of "collision" integral
is introduced for the description of diffusion in a system of particles, which
can transfer from a moving state to the rest state (with some waiting time
distribution). The solution of the appropriate kinetic equation in the external
field also confirms the phenomenological approach of the generalized master
equation.
