  For the fractional action cosmological model, derived earlier by the author
from the variational principle for a fractional action functional, the exact
solutions are obtained. The case of a quasi - vacuum state of matter that fills
the universe is considered. Moreover, on the basis of specific ansatz proposed
in this paper for the cosmological term, the class of exact solutions of the
model equations is obtained. Examples for some given laws of the cosmological
term evolution are provided. Besides, a formula for the effective equation of
state is derived, and the deceleration parameter of the obtained models is
studied.
