Fractional differential kinetics of dispersive transport as the consequence of its self-similarity

Analysis of the experimental data on anomalous transport in disordered semiconductors reveals a universal behavior of the transient photocurrent, which indicates the self-similarity of the transport process. The kinetic equations of the process, which contain a time derivative of a fractional order α ∈ (0, 1), have been derived on the basis of the self-similarity principle. These equations satisfy the “correspondence principle”: in the limit α → 1, they are transformed to the normal-diffusion equations. The solutions of the equations with fractional derivatives are expressed in terms of stable densities and are in good agreement with the experimental data.