  We analyze the cosmological solutions of $f(T,B)$ gravity using dynamical
system analysis where $T$ is the torsion scalar and $B$ be the boundary term
scalar. In our work, we assume two specific cosmological models. For first
model, we consider $ f(T,B)=f_{0}(B^{k}+T^{m})$, where $k$ and $m$ are
constants. For second model, we consider $f(T,B)=f_{0}T B$. We generate an
autonomous system of differential equations for each models by introducing new
dimensionless variables. To solve this system of equations, we use dynamical
system analysis. We also investigate the critical points and their natures,
stability conditions and their behaviors of Universe expansion. For both
models, we get four critical points. The phase plots of this system are
analyzed in detail and study their geometrical interpretations also. In both
model, we evaluated density parameters such as $\Omega_{r}$, $\Omega_{m}$,
$\Omega_{\Lambda}$ and $\omega_{eff}$ and deceleration parameter $(q)$ and find
their suitable range of the parameter $\lambda$ for stability. For first model,
we get $\omega_{eff}=-0.833,-0.166$ and for second model, we get
$\omega_{eff}=-\frac{1}{3}$. This shows that both the models are in
quintessence phase. Further, we compare the values of EoS parameter and
deceleration parameter with the observational values.
