Comments on various extensions of the Riemann–Liouville fractional derivatives : About the Leibniz and chain rule properties

Anna Szafrańska; Jacky Cresson

doi:10.1016/j.cnsns.2019.104903

Comments on various extensions of the Riemann–Liouville fractional derivatives : About the Leibniz and chain rule properties

Abstract

Starting from the Riemann–Liouville derivative, many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated analogue of the Leibniz relation. Discussing in full generality the existence of such operator over continuous functions, we derive some obstruction Lemma which can be used to prove the triviality of some operators as long as the linearity and the Leibniz property are preserved. As an application, we discuss some properties of the Jumarie’s fractional derivative as well as the local fractional derivative. We also discuss the chain rule property in the same perspective.

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Category:: Articles
Type:: artykuły w czasopismach
Published in:: Communications in Nonlinear Science and Numerical Simulation no. 82, pages 1 - 9,
ISSN: 1007-5704
Language:: English
Publication year:: 2020
Bibliographic description:: Szafrańska A., Cresson J.: Comments on various extensions of the Riemann–Liouville fractional derivatives : About the Leibniz and chain rule properties// Communications in Nonlinear Science and Numerical Simulation -Vol. 82, (2020), s.1-9
DOI:: Digital Object Identifier (open in new tab) 10.1016/j.cnsns.2019.104903
Verified by:: Gdańsk University of Technology