Fractional Calculus of Periodic Distributions
نویسنده
چکیده
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 Grünwald-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 discussed. AMS subject classifications: 26A33, 46F05, 47A70, 47D03 Abbreviated Title: Fractional Calculus.
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