Generalized Chapman-Kolmogorov equation: A unifying approach to the description of anomalous transport in external fields

The generalized Chapman-Kolmogorov equation [V. M. Kenkre, E. W. Montroll, and M. F. Shlesinger, J. Stat. Phys. 9, 45 (1973)] is discussed. It is demo nstrated that this equation unifies recently proposed kinetic equations of fractional order that describe anomalous transport in external fields, as w ell as continuous time random walks. The conditions under which the individ ual models can be established are discussed.