What is a fractional derivative?

Manuel D. Ortigueira, J. A. Tenreiro Machado

Research output: Contribution to journalArticlepeer-review

212 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 languageEnglish
Pages (from-to)4-13
Number of pages10
JournalJournal of Computational Physics
Volume293
Issue numberSI
DOIs
Publication statusPublished - Jul 2015

Keywords

  • Fractional calculus
  • Fractional derivative
  • Riesz potential

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