  A general analytic solution to the fractional advection diffusion equation is
obtained in plane parallel geometry. The result is an infinite series of
spatial Fourier modes which decay according to the Mittag-Leffler function,
which is cast into a simple closed form expression in Laplace space using the
Poisson summation theorem. An analytic expression for the current measured in a
time-of-flight experiment is derived, and the sum of the slopes of the two
respective time regimes on logarithmic axes is demonstrated to be -2, in
agreement with the well known result for a continuous time random walk model.
The sensitivity of current and particle number density to variation of
experimentally controlled parameters is investigated in general, and the
results applied to analyze selected experimental data.
