Fractional differentiation of devil's staircases

https://doi.org/10.1016/0378-4371(92)90573-9Get rights and content

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.

References (12)

  • J.B. Sokoloff

    Physics Rep.

    (1985)
  • S. Aubry et al.

    Physica D

    (1983)
  • B.B. Mandelbrot

    The Fractal Geometry of Nature

    (1983)
  • K. Falconer

    Fractal Geometry

    (1990)
  • K.B. Oldham et al.

    The Fractional Calculus

    (1974)
  • D. Schechtman et al.

    Phys. Rev. Lett.

    (1985)
There are more references available in the full text version of this article.

Cited by (0)

View full text
Copyright © 1992 Published by Elsevier B.V.