Master equation with two times: Diffusion in external field

The master equation for diffusion involving two times applies to the problem of diffusion in a time-dependent (in general inhomogeneous) external field. 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 the function of instantaneous displacements. For relatively weak external field the linear expansion of the PTD function leads to a simple generalization of diffusion equation, containing the retardation factors.