  The temporal Fokker-Plank equation [{\it J. Stat. Phys.}, {\bf 3/4}, 527
(2003)] or propagation-dispersion equation was derived to describe diffusive
processes with temporal dispersion rather than spatial dispersion as in
classical diffusion. %\cite{boon-grosfils-lutsko}. We present two
generalizations of the temporal Fokker-Plank equation for the first passage
distribution function $f_j(r,t)$ of a particle moving on a substrate with time
delays $\tau_j$. Both generalizations follow from the first visit master
equation. In the first case, the time delays depend on the local concentration,
that is the time delay probability $P_j$ is a functional of the particle
distribution function and we show that when the functional dependence is of the
power law type, $P_j \propto f_j^{\nu - 1}$, the generalized Fokker-Plank
equation exhibits a structure similar to that of the nonlinear spatial
diffusion equation where the roles of space and time are reversed. In the
second case, we consider the situation where the time delays are distributed
according to a power law, $P_j \propto \tau_j^{-1-\alpha}$ (with $0 < \alpha <
2$), in which case we obtain a fractional propagation-dispersion equation which
is the temporal analog of the fractional spatial diffusion equation (with space
and time interchanged).
