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On the Fractional Integrals of the Weierstrass Functions: the Exact Box Dimension

Zhou, Songping and Yao, K. (2002) On the Fractional Integrals of the Weierstrass Functions: the Exact Box Dimension. [Preprint]

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      Abstract

      The present paper investigates the fractal structure of the fractional integrals of the Weierstrass functions. The exact box dimension for many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas could be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.

      Item Type: Preprint
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: fractal, fractional calculus, Weierstrass function, box dimension
      Subjects: 28-xx Measure and integration > 28Axx Classical measure theory
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 20 Nov 2003
      Last Modified: 19 Aug 2010 15:00
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/125

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