Fractional Einstein-Hilbert Action Cosmology

Abstract: We propose a new type of cosmological model derived from the fractional variational principle when it is applied to the gravitational sector of action functional. In contrast to the fractional cosmological model developed earlier by the author from a fractional total action, in our new model the continuity equation remains valid in its usual form. For this model, a lot of exact solutions are obtained from a specific ansatz which is proposed for the cosmological term in this paper. Several examples arising from the given variations of the Hubble parameter with time are provided. Besides, we suggest an original interpretation of the main equations for our model. It supposes that the effective cosmological term could arise as a result of kinematical induction through the non-zero Hubble parameter. With the help of particular example, we demonstrate how this approach could lead our model quite closer to the real behavior of the universe.