Comments on various extensions of the Riemann-Liouville fractional derivatives: about the Leibniz and chain rule properties
type: Item
instance of: scholarly article
title: Comments on various extensions of the Riemann-Liouville fractional derivatives: about the Leibniz and chain rule properties
zbMATH Open document ID: 1451.26008
author: Jacky Cresson
author: Anna Szafrańska
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2020-10-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/1607.02571
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 49M25
Mathematics Subject Classification ID: 65Q30
zbMATH DE Number: 7265046
zbMATH Keywords: fractional derivations
zbMATH Keywords: Leibniz property
zbMATH Keywords: chain rule
zbMATH Keywords: obstruction lemma
zbMATH Keywords: Jumarie fractional derivative
zbMATH Keywords: local fractional derivative
MaRDI profile type: Publication
OpenAlex ID: W2963577058
Wikidata QID: Q123116836
arXiv ID: 1607.02571
cites work: Fractional variational calculus for nondifferentiable functions
cites work: The chain rule as a functional equation
cites work: About non-differentiable functions
cites work: Fractional differential equations and the Schrödinger equation
cites work: On calculus of local fractional derivatives
cites work: On the local fractional derivative
cites work: Scale calculus and the Schrödinger equation
cites work: A comment on some new definitions of fractional derivative
cites work: Q5732712
cites work: Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable. functions. Further results
cites work: Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions
cites work: Q5699297
cites work: Fractional differentiability of nowhere differentiable functions and dimensions
cites work: Q4438537
cites work: Characterizing the derivative and the entropy function by the Leibniz rule
cites work: Operator Relations Characterizing Derivatives
cites work: Counterexamples on Jumarie's two basic fractional calculus formulae
cites work: On the local fractional derivative of everywhere non-differentiable continuous functions on intervals
cites work: Counterexamples on Jumarie's three basic fractional calculus formulae for non-differentiable continuous functions
cites work: What is a fractional derivative?
cites work: Functions that have no first order derivative might have fractional derivatives of all orders less than one
cites work: Q3141895
cites work: No violation of the Leibniz rule. No fractional derivative
cites work: On chain rule for fractional derivatives
DOI: 10.1016/J.CNSNS.2019.104903
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description: scientific article