Analysis of $f(R)$ Theory Corresponding to NADE and NHDE

Abstract: We develop the connection of $f(R)$ theory with new agegraphic and holographic dark energy models. The function $f(R)$ is reconstructed, regarding the $f(R)$ theory as an effective description for these dark energy models. We show the future evolution of $f$ and conclude that these functions represent distinct pictures of cosmological eras. The cosmological parameters such as equation of state parameter, deceleration parameter, statefinder diagnostic and $\omega-\omega'$ analysis are investigated which assure the evolutionary paradigm of $f$.