  This paper studies the cosmology of accelerating expansion of the universe in
modified teleparallel gravity theory. We discuss the cosmology of $f(T,B)$
gravity theory and its implication to the new general form of the equation of
state parameter $w_{TB}$ for explaining the late-time accelerating expansion of
the universe without the need for the cosmological constant scenario. We
examine the numerical value of $w_{TB}$ in different paradigmatic $f(T,B)$
gravity models. In those models, the numerical result of $w_{TB}$ is favored
with observations in the presence of the torsion scalar T associated with a
boundary term B and shows the accelerating expansion of the universe.
