Desiderata for Fractional Derivatives and Integrals

By Rudolf Hilfer, Yuri Luchko. Mathematics, 2019

106 citations recorded by the source corpus.

The purpose of this brief article is to initiate discussions in this special issue by proposing desiderata for calling an operator a fractional derivative or a fractional integral. Our desiderata are neither axioms nor do they define fractional derivatives or integrals uniquely. Instead they intend to stimulate the field by providing guidelines based on a small number of time honoured and well established criteria.

Subfields: Computational Theory and Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/760148ddc525217607acc4b98f51b511cc0b442a

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Citations in the corpus

On a Fractional Operator Combining Proportional and Classical Differintegrals (2020, background): “It was first introduced as a conformable fractional derivative, but it lacks some of the desired properties for fractional derivatives [14].”
Why fractional derivatives with nonsingular kernels should not be used (2020, background): “g a non-singular kernel in the RL and Caputo derivatives can really be described as derivatives. While several papers make systematic attempts to determine whether or not a new operator is fractional [13,20,21,29,30], to the best of our knowledge very few attempts have been made to discern whether o”
Fractional derivatives and the fundamental theorem of fractional calculus (2020, unknown): “, a linear operator is called a fractional derivative if and only if it is a left-inverse operator to the Riemann-Liouville fractional integral on a certain space of functions (compare to the desiderata (c) from [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.”