  Considering the large number of fractional operators that exist, and since it
does not seem that their number will stop increasing soon at the time of
writing this paper, it is presented for the first time, as far as the authors
know, a simplified and compact way to work the fractional calculus through the
classification of fractional operators using sets. This new way of working with
fractional operators, which may be called as fractional calculus of sets,
allows to generalize objects of the conventional calculus such as tensor
operators, the diffusion equation, the heat equation, the Taylor series of a
vector-valued function, and the fixed point method in several variables which
allows to generate the method known as the fractional fixed point method. It is
also shown that each fractional fixed point method that generates a convergent
sequence has the ability to generate an uncountable family of fractional fixed
point methods that generate convergent sequences. So, it is shown one way to
estimate numerically the mean order of convergence of any fractional fixed
point method in a region $\Omega$ through the problem of determining the
critical points of a scalar function, and it is shown how to construct a hybrid
fractional iterative method to determine the critical points of a scalar
function.
