Counterexamples on Jumarie's three basic fractional calculus formulae for non-differentiable continuous functions

DOI10.1016/j.chaos.2018.02.036zbMath1390.26011arXiv1611.05099OpenAlexW2582224925WikidataQ124819272 ScholiaQ124819272MaRDI QIDQ1636977

Cheng-Shi Liu

Publication date: 7 June 2018

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.05099

zbMATH Keywords

counterexamplefractional calculusmodified Riemann-Liouville derivativeJumarie formulae

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33)

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Cites Work

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• No violation of the Leibniz rule. No fractional derivative
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• Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions
• On the local fractional derivative of everywhere non-differentiable continuous functions on intervals
• On chain rule for fractional derivatives
• The extended trial equation method for some time fractional differential equations
• The modified trial equation method for fractional wave equation and time fractional generalized Burgers equation
• Fractional calculus: D'où venons-nous? Que sommes-nous? Où allons-nous? (Contributions to Round Table Discussion held at ICFDA 2016)
• Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable. functions. Further results
• New stochastic fractional models for Malthusian growth, the Poissonian birth process and optimal management of populations
• On the representation of fractional Brownian motion as an integral with respect to \((dt)^a\)
• On the solution of the stochastic differential equation of exponential growth driven by fractional Brownian motion

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