A novel approach using equations with fractional order derivatives to describe dispersive transport in disordered semiconductors is described. A relationship between the self-similarity of dispersive transport, stable limiting distributions, and kinetic equations with fractional derivatives is established. It is shown that unlike the well-known Scher — Montroll and Arkhipov — Rudenko models, which are in a sense alternatives to the normal transport model, fractional differential equations provide a unified mathematical framework for describing normal and dispersive transport. The fractional differential formalism allows the equations of ambipolar dispersive transport to be written down and transport in systems with a distributed dispersion parameter to be described. The relationship between fractional differential equations and the generalized limiting theorem reveals the probabilistic aspects of the phenomenon in which a dispersive-to-Gaussian transport transition occurs in a time-of-flight experiment as the applied voltage is decreased and/or the sample thickness increased.

@article{Sibatov:2009,
	author = {R. T. Sibatov and V. V. Uchaikin},
	title = {Fractional differential approach to dispersive transport in semiconductors},
	publisher = {Physics-Uspekhi},
	year = {2009},
	journal = {Phys. Usp.},
	volume = {52},
	number = {10},
	pages = {1019-1043},
	url = {https://ufn.ru/en/articles/2009/10/c/},
	doi = {10.3367/UFNe.0179.200910c.1079}
}