  There are many possible definitions of derivatives, here we present some and
present one that we have called generalized that allows us to put some of the
others as a particular case of this but, what interests us is to determine that
there is an infinite number of possible definitions of fractional derivatives,
all are correct as differential operators each of which must be properly
defined in its algebra.
  We introduce a generalized version of the fractional derivative that extends
the existing ones in the literature. To those extensions, it is associated with
a differentiable operator and a differential ring and applications that show
the advantages of the generalization.
  We also review the different definitions of fractional derivatives proposed
by Michele Caputo in \cite{GJI:GJI529}, Khalil, Al Horani, Yousef, Sababheh in
\cite{khalil2014new}, Anderson and Ulness in \cite{anderson2015newly}, Guebbai
and Ghiat in \cite{guebbai2016new}, Udita N. Katugampola in
\cite{katugampola2014new}, Camrud in \cite{camrud2016conformable} and it is
shown how the generalized version contains the previous ones as a particular
case.
