Fractional differentiation of devil's staircases

H.J. Schellnhuber and A. Seyler

Physica A: Statistical Mechanics and its Applications, 1992, vol. 191, issue 1, 491-500

Abstract: Modern nonlinear dynamics abounds in mathematical objects with bizarre shapes and properties. It is argued that fractional calculus provides powerful tools for the description of such “monstrosities”. The application of generalized differintegration to devil's staircases is discussed in detail. On the basis of these results, an extension of the conventional classification scheme for phase transitions, introducing fractional order, is proposed.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:191:y:1992:i:1:p:491-500

DOI: 10.1016/0378-4371(92)90573-9

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