In this paper, based on a physical picture of the unified theory of the low frequency fluctuation, dissipation and relaxation phenomenon, some transport features of a non-Markovian process are explored. It is found that: (1) due to the effect of infrared divergence the diffusion coefficient, the mobility, and the viscosity as well as the generalized MD relation (MD) (i.e., Nernst-Einstein relation) and the generalized DV relation (DV) which exist among these coefficients, in general, are dispersive and the degree of the dispersion depends on a single parameter n, the infrared divergence exponent. If n goes to zero, all results immediately reduce to the classical forms; (2) the MV relation, neither depending on the nature of the transport process nor on the structure of the medium, seems to be generally valid and (3) the functional form of the generalized diffusion coefficient is identical with that of the generalized mobility, and that of the MD relation with that of the DV relation. The prediction of the dispersive diffusion is in good agreement with the recent experiment. The MD relation has been surmised ought to exist. If it exists, the prediction of dispersive mobility would be true.