An introduction to fractional calculus. (English) Zbl 0987.26005

Butzer, P. L.; Westphal, U.

Hilfer, R. (ed.), Applications of fractional calculus in physics. Singapore: World Scientific. 1-85 (2000).

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.
For the entire collection see [Zbl 0998.26002].

Reviewer: Ram Kishore Saxena (Jodhpur)

MSC:

26A33	Fractional derivatives and integrals
26-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
44A15	Special integral transforms (Legendre, Hilbert, etc.)

Keywords:

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