On Fractional Operators and Their Classifications

By Dumitru Băleanu, Arran Fernandez. Mathematics, 2019

213 citations recorded by the source corpus.

Fractional calculus dates its inception to a correspondence between Leibniz and L’Hopital in 1695, when Leibniz described “paradoxes” and predicted that “one day useful consequences will be drawn” from them. In today’s world, the study of non-integer orders of differentiation has become a thriving field of research, not only in mathematics but also in other parts of science such as physics, biology, and engineering: many of the “useful consequences” predicted by Leibniz have been discovered. However, the field has grown so far that researchers cannot yet agree on what a “fractional derivative” can be. In this manuscript, we suggest and justify the idea of classification of fractional calculus into distinct classes of operators.

Subfields: Mathematical Physics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a972717973e142b386e7b046f6a83007a0fc3ae8

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Citations in the corpus

On a Fractional Operator Combining Proportional and Classical Differintegrals (2020, background): “These diverse definitions may be categorised into general classes according to their structure and properties [11].”
Weighted Fractional Calculus: A General Class of Operators (2022, background): “The more recent definitions are too numerous to list here, but we refer to [12, 27] for some surveys of examples, and to [5] for a description of the philosophy of classification of operators in fractional calculus.”
On tempered fractional calculus with respect to functions and the associated fractional differential equations (2021, background): “In terms of mathematical properties, the many different types of operators can generally be gathered into a few broad classes [7].”