  We present a general phase-space kinetic model for charged particle transport
through combined localised and delocalised states, capable of describing
scattering collisions, trapping, detrapping and losses. The model is described
by a generalised Boltzmann equation, for which an analytical solution is found
in Fourier-Laplace space. The velocity of the centre of mass (CM) and the
diffusivity about it are determined analytically, together with the flux
transport coefficients. Transient negative values of the free particle CM
transport coefficients can be observed due to the trapping to, and detrapping
from, localised states. A Chapman-Enskog type perturbative solution technique
is applied, confirming the analytical results and highlighting the emergence of
a density gradient representation in the weak-gradient hydrodynamic regime. A
generalised diffusion equation with a unique global time operator is shown to
arise, reducing to the standard diffusion equation and a Caputo fractional
diffusion equation in the normal and dispersive limits. A subordination
transformation is used to solve the generalised diffusion equation by mapping
from the solution of a corresponding standard diffusion equation.
