Fractional calculus of periodic distributions

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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 (https://doi.org/10.2478/s13540-011-0016-6)

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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

Khan, Khaula Naeem, Lamb, Wilson ORCID logoORCID: https://orcid.org/0000-0001-8084-6054 and Mcbride, Adam;
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