Abstract
The purpose of this paper is to give a simple development of the Weyl fractional transform W−v, and to establish some of its elementary properties. In particular, we shall define the Weyl fractional derivative Wv and show that
for all α and β, positive, negative, or zero. We also indicate briefly its relationship to the Hadamard finite part of an improper integral.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Erdélyi, Tables of Integral Transforms, Volume II, McGraw-Hill, 1954.
J. Hadamard, Lectures on Cauchy's problem in Linear Partial Differential Equations, Dover Publications, 1952.
M. J. Lighthill, Introduction to Fourier Analysis and Generalised Functions, Cambridge University Press, 1959.
K. S. Miller, Linear Differential Equations in the Real Domain, W. W. Norton, 1963.
Editor information
Rights and permissions
Copyright information
© 1975 Springer-Verlag
About this chapter
Cite this chapter
Miller, K.S. (1975). The weyl fractional calculus. In: Ross, B. (eds) Fractional Calculus and Its Applications. Lecture Notes in Mathematics, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067098
Download citation
DOI: https://doi.org/10.1007/BFb0067098
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07161-7
Online ISBN: 978-3-540-69975-0
eBook Packages: Springer Book Archive