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A distributional theory of fractional calculus

Published online by Cambridge University Press:  14 November 2011

W. Lamb
W. Lamb
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow
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Synopsis

In this paper, a theory of fractional calculus is developed for certain spaces D′p,μ of generalised functions. The theory is based on the construction of fractionalpowers of certain simple differential and integral operators. With the parameter μ suitably restricted, these fractional powers are shown to coincide with the Riemann-Liouville and Weyl operators of fractional integration and differentiation. Standard properties associated with fractional integrals and derivatives follow immediately from results obtained previously by the author on fractional powers of operators; see [6], [7]. Some spectral properties are also obtained.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 99 , Issue 3-4 , 1985 , pp. 347 - 357
Copyright
Copyright © Royal Society of Edinburgh 1985

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