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

    Creators(s): Khan, Khaula Naeem, Lamb, Wilson ORCID logoORCID: https://orcid.org/0000-0001-8084-6054 and Mcbride, Adam;
    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:01 Jan 2021 09:44
    URI:https://strathprints.strath.ac.uk/id/eprint/30368
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