Reconstruction of $f(R)$, $f(T)$ and $f(\mathcal{G})$ models inspired by variable deceleration parameter

We study an special law for the deceleration parameter, recently proposed by Akarsu and Dereli, in the context of $f(R)$, $f(T)$ and $f(\mathcal{G})$ theories of modified gravity. This law covers the law of Berman for obtaining exact cosmological models to account for the current acceleration of the universe, and also gives the opportunity to generalize many of the dark energy models having better consistency with the cosmological observations. Our aim is to reconstruct the $f(R)$, $f(T)$ and $f(\mathcal{G})$ models inspired by this law of variable deceleration parameter. Such models may then exhibit better consistency with the cosmological observations.