Fractional calculus of periodic distributions

Khaula Naeem Khan, Wilson Lamb, Adam Mcbride

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
150 Downloads (Pure)


Two approaches for defining fractional derivatives of periodic distributions
are presented. The first is a distributional version of the Weyl fractional derivative in which a derivative of arbitrary order of a periodic distribution is defined via Fourier series. The second is based on the Gr¨unwald-Letnikov formula for defining a fractional derivative as a limit of a fractional difference quotient. The equivalence of the two approaches is established and an application to a fractional diffusion equation, posed in a space of periodic distributions, is also discusse
Original languageEnglish
Pages (from-to)260-283
Number of pages24
JournalFractional Calculus and Applied Analysis
Issue number2
Publication statusPublished - 2011


  • fractional derivatives
  • distributions
  • fractional integrals

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