  The unified description of diffusion processes that cross over from a
ballistic behavior at short times to normal or anomalous diffusion (sub- or
superdiffusion) at longer times is constructed on the basis of a non-Markovian
generalization of the Fokker-Planck equation. The necessary non-Markovian
kinetic coefficients are determined by the observable quantities (mean- and
mean square displacements). Solutions of the non-Markovian equation describing
diffusive processes in the physical space are obtained. For long times, these
solutions agree with the predictions of the continuous random walk theory; they
are, however, much superior at shorter times when the effect of the ballistic
behavior is crucial.
