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A note on the index laws of fractional calculus

Part of: Real functions

Published online by Cambridge University Press:  09 April 2009

Adam C. Mcbride
Adam C. Mcbride
Affiliation:
Department of Mathematics University of StrathclydeLivingstone Tower 26 Richmond Street, Glasgow GI 1XH Scotland, U.K.
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Abstract

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Two index laws for fractional integrals and derivatives, which have been extensively studied by E. R. Love, are shown to be special cases of an index law for general powers of certain differential operators, by means of the theory developed in a previous paper. Discussion of the two index laws, which are rather different in appearance, can thus be unified.

MSC classification

Secondary: 26A33: Fractional derivatives and integrals
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 3 , June 1983 , pp. 356 - 363
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Erdélyi, A., ‘Fractional integrals of generalised functions’, J. Austral. Math. Soc. 14 (1972), 30–37.CrossRefGoogle Scholar
[2]Love, E. R., ‘Two index laws for fractional integrals and derivatives’, J. Austral. Math. Soc. 14 (1972), 385–410.CrossRefGoogle Scholar
[3]McBride, A. C., Fractional calculus and integral transforms of generalised functions, Research Notes in Mathematics No. 31 (Pitman, London, 1979).Google Scholar
[4]McBride, A. C., ‘Fractional powers of a class of ordinary differential operators’, Proc. London Math. Soc. (3), to appear.Google Scholar