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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

Item type: Article
ID code: 30368
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: 16 Oct 2017 10:24
URI: https://strathprints.strath.ac.uk/id/eprint/30368
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