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Fundamental properties of fractional derivatives via pochhammer integrals

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Fractional Calculus and Its Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 457))

Abstract

In this paper, various representations of fractional differentiation are explored, and a definition using Pochhammer contour integrals emerges as deserving special emphasis. The analyticity of Dαzpf(z) and Dαzpln z f(z) is investigated with reference to the three variables z, α, and p. The validity of the operation DβDα=Dα+α is studied. An improvement in the Leibniz rule for the fractional derivative of the product of two functions published previously is given.

Supported by N.R.C. Grant A4027.

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Authors
  1. J. L. Lavoie
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  2. R. Tremblay
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  3. T. J. Osler
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Editor information

Bertram Ross

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© 1975 Springer-Verlag

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Lavoie, J.L., Tremblay, R., Osler, T.J. (1975). Fundamental properties of fractional derivatives via pochhammer integrals. In: Ross, B. (eds) Fractional Calculus and Its Applications. Lecture Notes in Mathematics, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067118

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  • DOI: https://doi.org/10.1007/BFb0067118

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07161-7

  • Online ISBN: 978-3-540-69975-0

  • eBook Packages: Springer Book Archive

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