  Velocity autocorrelation functions (VAF) of the fluids are studied on short-
and long-time scales within a unified approach. This approach is based on an
effective summation of the infinite continued fraction at a reasonable
assumption about convergence of relaxation times of the high order memory
functions, which have purely kinetic origin. The VAFs obtained within our
method are compared with computer simulation data for the liquid Ne at
different densities and the results, which follow from the Markovian
approximation for the highest order kinetic kernels. It is shown that in all
the thermodynamic points and at the chosen level of the hierarchy, our results
agree much better with the MD data than those of the Markovian approximation.
The density dependence of the transition time, needed for the fluid to attain
the hydrodynamic stage of evolution, is evaluated. The common and distinctive
features of our method are discussed in their relations to the generalized
collective mode (GCM) theory, the mode coupling theory (MCT), and some other
theoretical approaches.
