广义分数导数，分数微分环
Generalized Fractional Derivative, Fractional differential ring
摘要：
有许多可能的定义的衍生物，在这里我们提出了一些和目前的一个，我们已经呼吁广义，使我们能够把一些其他作为一个特殊的情况下，但我们感兴趣的是，以确定有无限数量的可能定义的分数导数，所有正确的微分算子，其中每一个必须正确定义在其代数。我们引入了一个广义版本的分数阶导数，扩展了现有的文献中。对于这些推广，它与一个可微算子和一个微分环相关联，并展示了推广的优点。我们还回顾了Michele Caputo在\cite{GJI:GJI529}中，Khalil，Al Horani，Yousef，Sababheh在\cite{khalil2014new}中，Anderson和Ulness在\cite{anderson2015newly}中，Guebbai和Ghiat在\cite{guebbai2016new}中，Udita N. Katugampola在\cite{katugampola2014new}中，Camrud在\cite{camrud2016conformable}中，它显示了如何广义版本包含以前的作为一个特定的情况。
英文摘要：
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.
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