Constraints on the parameters of modified Chaplygin-Jacobi and modified Chaplygin-Abel gases in $f(T)$ gravity

In this study, we investigate two dark energy models, MCJG and MCAG, in the context of $f(T)$ gravity within a non-flat FLRW Universe. Our analysis considers radiation, dark matter, and dark energy components. We compare the equation of state for MCJG and MCAG with $f(T)$ gravity. Using recent astronomical data (e.g., $H(z)$, type Ia supernovae, Gamma Ray Bursts, quasars, and BAO), we constrain the models' parameters and explore the Universe's behavior. The reduced Hubble parameter is expressed in terms of observable parameters like $\Omega_{r0}$, $\Omega_{m0}$, $\Omega_{k0}$, $\Omega_{CJ0}$, $\Omega_{CA0}$, and $H_0$. We investigate cosmic evolution using deceleration, $\mathrm{Om}$, and statefinder diagnostics. Information criteria are employed to assess model viability, comparing against the standard $\Lambda$CDM model. Our objective is to deepen our understanding of dark energy, its relation to $f(T)$ gravity, and the mechanisms governing the accelerated expansion of the Universe.