  An analysis of a fractional cubic differential equation is presented, which
is a generalization of different versions of fractional logistic equations, in
order to obtain simpler numerical methods that globalize and extend the results
already obtained, and allow the comparison between several methods. The
existence and uniqueness of the solution of the fractional cubic problem
subject to an initial value are demonstrated, a stability analysis is performed
and, based on the implementation of numerical methods, a comparison is made
between the different logistic models.
