What is a fractional derivative?

Manuel D. Ortigueira, J. A. Tenreiro Machado

Research output: Contribution to journalArticle

178 Citations (Scopus)


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
Issue numberSI
Publication statusPublished - Jul 2015


  • Fractional calculus
  • Fractional derivative
  • Riesz potential

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