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We study an special law for the deceleration parameter, recently proposed byAkarsu 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 obtainingexact cosmological models to account for the current acceleration of theuniverse, and also gives the opportunity to generalize many of the dark energymodels having better consistency with the cosmological observations. Our aim isto reconstruct the $f(R)$, $f(T)$ and $f(\mathcal{G})$ models inspired by thislaw of variable deceleration parameter. Such models may then exhibit betterconsistency with the cosmological observations.

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