A review of definitions of fractional derivatives and other operators

Abstract

Given the increasing number of proposals and definitions of operators in the scope of fractional calculus, it is important to introduce a systematic classification. Nonetheless, many of the definitions that emerged in the literature can not be considered as fractional derivatives. We analyze a list of expressions to have a general overview of the concept of fractional (integrals) derivatives. Moreover, some formulae that do not involve the term fractional, are also included due to their particular interest in the area.