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Zbl 0987.26005
Butzer, P.L.; Westphal, U.
An introduction to fractional calculus. (English)
[A] Hilfer, R. (ed.), Applications of fractional calculus in physics. Singapore: World Scientific. 1-85 (2000). ISBN 981-02-3457-0

This article deals with a brief historical survey of fractional calculus. It contains various definitions of fractional calculus given from time to time by various mathematicians. Applications to various special functions, such as Stirling function, Euler function, Bernoulli polynomials, etc. are demonstrated.
[Ram Kishore Saxena (Jodhpur)]
MSC 2000:
*26A33 Fractional derivatives and integrals (real functions)
26-01 Textbooks (real functions)
44A15 Special transforms

Keywords: fractional derivatives and integrals; Riemann-Liouville operator; semigroups; Leibniz rule; Mellin transform; Stirling function; Euler function; Bernoulli polynomials

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