### R. Hilfer

in: Handbook of Fractional Calculus with Applications: Basic Theory, Vol. 1

edited by: A. Kochubei and Y. Luchko

Walter de Gruyter GmbH, Berlin, 47-86 (2019)

https://doi.org/10.1515/9783110571622

ISBN: 9783110571622

submitted on

Saturday, June 2, 2018

Brief descriptions of various mathematical and physical interpretations of fractional derivatives and integrals have been collected into this chapter as points of reference and departure for deeper studies. “Mathematical interpretation” in the title means a brief description of the basic mathematical idea underlying a precise definition. “Physical interpretation” means a brief description of the physical theory underlying an identification of the fractional order with a known physical quantity. Numerous interpretations had to be left out due to page limitations. Only a crude, rough and ready description is given for each interpretation. For precise theorems and proofs an extensive list of references can serve as a starting point.

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