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In this work we use tempered fractional advection-diffusion equations to model the dispersive transport in disordered materials. A numerical method is derived to approximate the solution of such differential models and we prove that it is convergent and stable. Two numerical examples are presented. The first one, with known analytical solution, is given to illustrate the performance of the numerical scheme; the second one is used to show that such models are appropriate to model time of flight transient currents for some disordered materials.

Modeling Transient Currents in Time-of-Flight Experiments with Tempered Time-Fractional Diffusion Equations