Cosmological Dynamics of Accelerating Model in $f(T)$ Gravity with Special Forms of Deceleration Parameter

In this paper, the dynamical behavior of the accelerated expansion of the universe is discussed within the framework of $f(T)$ gravity, considering power law functional form of $f(T)=\alpha (-T)^{n}$. Two distinct redshift-dependent parameterization of the deceleration parameter such as $q(z)=q_{0}+ q_{1}\left(\frac{ \ln(N+z)}{z+1}-\ln N \right)$ and $q(z)=\frac{1}{2}+ \frac{q_{1}z+ q_{2}}{(1+z)^2}$ are considered. We have derived the Hubble parameter in terms of redshift and discussed its effect on other cosmological parameters. Using Bayesian statistical analysis and $\chi^2$-minimization, the median values of the model parameters for both the cosmic chronometer(CC) and the joint(CC + Pantheon) dataset have been determined. Further, energy density, pressure, the equation of state for Dark Energy, Energy condition and statefinder diagnostics are analyzed. The current age of the universe is also computed for these models.