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Anomalous (non-Gaussian) kinetics is often observed in various disordered materials, such as amorphous semiconductors, porous solids, polycrystalline films, liquid-crystalline materials, polymers, etc. Recently the anomalous relaxation-diffusion processes have been observed in nanoscale systems: nanoporous silicon, glasses doped by quantum dots, quasi-one-dimensional (1D) systems, arrays of colloidal quantum dots, and some others. The paper presents a review of new approach, based on fractional kinetic equations. We give a physical basis for some fractional equations deriving them from their classical counterparts by means of averaging over statistical ensemble of disordered media. We consider self-similarity as the main feature of these processes, and explain memory phenomena in frameworks of hidden variables conception.

The charge carrier transport in disordered semiconductors is described by making use of the fractional calculus. The physical reasons of introducing fractional derivatives in semiconductor theory are discussed, the process of derivation of fractional differential equations is demonstrated, solutions of fractional differential equations are represented in terms of one-sided stable distributions. The solutions are applied to multiple trapping phenomenon, transient photocurrent and drift mobility, dispersive transport percolation model, transport in bilayer semiconductor. Some numerical results are obtained and their agreement with experimental data is demonstrated.