  In this paper, we investigate $f(T)$ cosmology and find an exact solution for
$f$ which gives a Little Rip cosmology. Also, considering accelerating
cosmology with dark matter, the time-dependent solution is found. For these
cases, by using solutions obtained from $f(T)$ gravity we find expressions for
$\omega$ and $\Lambda$ defined as time functions via equivalent description in
terms of inhomogeneous fluid. This puts the question: which theoretical model
describes the observational cosmology?
