  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.
