A review of definitions of fractional derivatives and other operators. (English) Zbl 1452.26008
Summary: 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.
MSC:
| 26A33 | Fractional derivatives and integrals |
| 26A24 | Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems |
| 26-02 | Research exposition (monographs, survey articles) pertaining to real functions |
Keywords:
fractional calculus; fractional derivatives; fractional operators; local operators; operators with nonsingular kernelReferences:
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