Fractional differentiation of devil's staircases

✍ Scribed by H.J. Schellnhuber; A. Seyler

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 499 KB
• Volume: 191
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(92)90573-9

✦ Synopsis

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.