  In this paper, we investigate time-dependent Kantowski-Sachs spherically
symmetric teleparallel $F(T)$ gravity in vacuum and in a perfect isotropic
fluid. We begin by finding the field equations and solve for new teleparallel
$F(T)$ solutions. With a power-law ansatz for the coframe functions, we find
new non-trivial teleparallel $F(T)$ vacuum solutions. We then proceed to find
new non-trivial teleparallel $F(T)$ solutions in a perfect isotropic fluid with
both linear and non-linear equation of state. We find a great number of new
exact and approximated teleparallel $F(T)$ solutions. These classes of new
solutions are relevant for future cosmological applications.
