Fractional calculus of periodic distributions

Khaula Naeem Khan, Wilson Lamb, Adam Mcbride

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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
LanguageEnglish
Pages260-283
Number of pages24
JournalFractional Calculus and Applied Analysis
Volume14
Issue number2
DOIs
Publication statusPublished - 2011

Fingerprint

Fractional Calculus
Fractional Derivative
Derivatives
Fractional Diffusion Equation
Fourier series
Quotient
Fractional
Equivalence
Derivative
Arbitrary

Keywords

  • fractional derivatives
  • distributions
  • fractional integrals

Cite this

Khan, Khaula Naeem ; Lamb, Wilson ; Mcbride, Adam. / Fractional calculus of periodic distributions. In: Fractional Calculus and Applied Analysis . 2011 ; Vol. 14, No. 2. pp. 260-283.
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Fractional calculus of periodic distributions. / Khan, Khaula Naeem; Lamb, Wilson; Mcbride, Adam.

In: Fractional Calculus and Applied Analysis , Vol. 14, No. 2, 2011, p. 260-283.

Research output: Contribution to journalArticle

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T1 - Fractional calculus of periodic distributions

AU - Khan, Khaula Naeem

AU - Lamb, Wilson

AU - Mcbride, Adam

N1 - changed journal title

PY - 2011

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N2 - Two approaches for defining fractional derivatives of periodic distributionsare 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

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KW - distributions

KW - fractional integrals

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