Fractional calculus of periodic distributions

Khan, Khaula Naeem and Lamb, Wilson and Mcbride, Adam (2011) Fractional calculus of periodic distributions. Fractional Calculus and Applied Analysis, 14 (2). pp. 260-283. ISSN 1314-2224

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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

ORCID iDs

Lamb, Wilson ORCID: https://orcid.org/0000-0001-8084-6054

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  Item type:	Article
  ID code:	30368
  Dates:	Date Event 2011 Published
  Notes:	changed journal title
  Keywords:	fractional derivatives, distributions, fractional integrals, Probabilities. Mathematical statistics
  Subjects:	Science > Mathematics > Probabilities. Mathematical statistics
  Department:	Faculty of Science > Mathematics and Statistics
  Depositing user:	Pure Administrator
  Date deposited:	08 Apr 2011 12:15
  Last modified:	22 Oct 2021 00:23
  URI:	https://strathprints.strath.ac.uk/id/eprint/30368