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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Official URL: https://doi.org/10.2478/s13540-011-0016-6

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

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Khan, Khaula Naeem, Lamb, Wilson

and Mcbride, Adam;

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Item metadata

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:	23 Jan 2021 02:50
URI:	https://strathprints.strath.ac.uk/id/eprint/30368

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