  We construct models of interacting itinerant non-Abelian anyons moving along
one-dimensional chains, focusing in particular on itinerant Ising anyon chains,
and derive effective anyonic t-J models for the low energy sectors. Solving
these models by exact diagonalization, we find a fractionalization of the
anyons into charge and (non-Abelian) anyonic degrees of freedom -- a
generalization of spin-charge separation of electrons which occurs in Luttinger
liquids. A detailed description of the excitation spectrum by combining spectra
for charge and anyonic sectors requires a subtle coupling between charge and
anyonic excitations at the microscopic level (which we also find to be present
in Luttinger liquids), despite the macroscopic fractionalization.
