  In this work, we study a cosmological model of Bianchi type-I Universe in
teleparallel gravity for a perfect fluid. To obtain the cosmological solution
of the model, we assume that the deceleration parameter is a linear function of
the Hubble parameter $H$ i.e. $q=-1+\beta H$ (where $\beta $ as a positive
constant). Consequently, we get a model of our Universe, where it goes from the
initial phase of deceleration to the current phase of acceleration. We have
discussed some physical and geometric properties such as Hubble parameter,
deceleration parameter, energy density, pressure, and equation of state (EoS)
parameter and study their behavior graphically in terms of redshift and compare
it with observational data such as Type Ia supernovae (SNIa). We also discussed
the behavior of other parameters such as the Jerk parameter, Statefinder
parameters and we tested the validity of the model by studying the stability
analysis and energy conditions.
