A review of definitions of fractional derivatives and other operators

By G. Sales Teodoro, J. Machado, E. Capelas de Oliveira. Journal of Computational Physics, 2019

444 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9c65ae41d53c882f97d5135fb0a160bf8ad7418e

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Weighted Fractional Calculus: A General Class of Operators (2022, background): “As well as other classical definitions such as those of Riesz and Caputo, so many new definitions have been proposed in the 21st century [21,22] that it has become necessary to categorise them into general classes of operators for mathematical study [23].”
Nonlinear generalized fractional differential equations with generalized fractional integral conditions (2020, background): “A good review of different fractional operators can be found in [8].”