Testing a cosmological teleparallel modified f(T) model with parametric H(z)

We study the late-time cosmological expansion of a modified teleparallel gravity model. This modified gravitational lagrangian yields a cosmological constant term along with power-law corrections to the Teleparallel Equivalent of General Relativity (TEGR) for small $\lambda$. By combining observational data from cosmic chronometers, Type Ia supernovae from the Pantheon+ dataset, and Baryon Acoustic Oscillations (BAO) from DESI RD1, we constrain the parameters of the modified gravitational dynamics assuming a quadratically parameterized Hubble rate $H(z)$. The joint observational fit indicates a late-time accelerated expansion with a deceleration parameter of $q_0 = -0.417_{-0.022}^{+0.021}$. Furthermore, we analyze the effective energy density, pressure, and equation-of-state parameter $\omega$, showing that this modified gravity theory naturally accommodates quintessence like and phantom like behavior. Finally, a linear scalar perturbation analysis confirms that the cosmological background is dynamically stable against homogeneous fluctuations.