What is a fractional derivative?

Manuel D. Ortigueira; J. A. Tenreiro Machado

doi:10.1016/j.jcp.2014.07.019

What is a fractional derivative?

Manuel D. Ortigueira, J. A. Tenreiro Machado

Research output: Contribution to journal › Article › peer-review

294 Citations (Scopus)

Abstract

This paper discusses the concepts underlying the formulation of operators capable of being interpreted as fractional derivatives or fractional integrals. Two criteria for required by a fractional operator are formulated. The Grünwald-Letnikov, Riemann-Liouville and Caputo fractional derivatives and the Riesz potential are accessed in the light of the proposed criteria. A Leibniz rule is also obtained for the Riesz potential.

Original language	English
Pages (from-to)	4-13
Number of pages	10
Journal	Journal of Computational Physics
Volume	293
Issue number	SI
DOIs	https://doi.org/10.1016/j.jcp.2014.07.019
Publication status	Published - Jul 2015

Keywords

Fractional calculus
Fractional derivative
Riesz potential

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10.1016/j.jcp.2014.07.019Licence: CC BY-NC-ND

Cite this

@article{e307673516ea41d583de93d3ed639aa8,

title = "What is a fractional derivative?",

abstract = "This paper discusses the concepts underlying the formulation of operators capable of being interpreted as fractional derivatives or fractional integrals. Two criteria for required by a fractional operator are formulated. The Gr{\"u}nwald-Letnikov, Riemann-Liouville and Caputo fractional derivatives and the Riesz potential are accessed in the light of the proposed criteria. A Leibniz rule is also obtained for the Riesz potential.",

keywords = "Fractional calculus, Fractional derivative, Riesz potential",

author = "Ortigueira, {Manuel D.} and {Tenreiro Machado}, {J. A.}",

note = "Sem PDF. This work was partially funded by National Funds through the Foundation for Science and Technology of Portugal, under the project PEst-OE/EEI/UI0066/2011. We thank to Carl F. Lorenzo for the suggesting the fractional derivative concept.",

year = "2015",

month = jul,

doi = "10.1016/j.jcp.2014.07.019",

language = "English",

volume = "293",

pages = "4--13",

journal = "Journal of Computational Physics",

issn = "0021-9991",