Reconstructing f(T) modified gravity from ECHDE and ECNADE models

We investigate alternative candidates to dark energy (DE) that can explain the current state of the Universe in the framework of the generalized teleparallel theory of gravity f(T), where T denotes the torsion scalar. To achieve this, we carry out a series of reconstructions taking into account the ordinary and entropy-corrected versions of the holographic and new agegraphic DE models. These models are used as alternatives to DE in the literature in order to describe the current state of our Universe. It is remarked that the proposed models indicate behavior akin to phantom or quintessence models. Furthermore, we also generate the parameters of the equation of state associated with entropy-corrected models and we observe a phase transition between the quintessence state and phantom state as it is shown by the recent observational data. We also investigate the stability of these models and we create the $\{r-s\}$ trajectories and compare with the ΛCDM limit. The behavior of certain physical parameters such as the speed of sound and the Statefinder diagnostic pair $\{r-s\}$ is compatible with the current observational data.