  We use a particular fractional generalization of the ordinary differential
equations that we apply to the Riccati equation of constant coefficients. By
this means the latter is transformed into a modified Riccati equation with the
free term expressed as a power of the independent variable which is of the same
order as the order of the applied fractional derivative. We provide the
solutions of the modified equation and employ the results for the case of the
cosmological Riccati equation of FRW barotropic cosmologies that has been
recently introduced by Faraoni
