Local Fractional Derivatives and Fractal Functions of Several Variables

Abstract

The notion of a local fractional derivative (LFD) was introduced recently for functions of a single variable. LFD was shown to be useful in studying fractional differentiability properties of fractal and multifractal functions. It was demonstrated that the local Holder exponent/ dimension was directly related to the maximum order for which LFD existed. We have extended this definition to directional-LFD for functions of many variables and demonstrated its utility with the help of simple examples.

arXiv comment4 pages, Revtex, appeared in proceedings of 'Fractals in Engineering' Arcachon, France (1997)

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