Holder exponents of irregular signals and local fractional derivatives

Details Holder exponents of irregular signals and local fractional derivatives Holder exponents of irregular signals and local fractional derivatives

1997-11-09

arxiv.org/abs/chao-dyn/9711010v1

Pramana - J. Phys. 48 (1997) 49

Nonlinear Sciences

Chaotic Dynamics

20 pages, Latex

Scientific paper

10.1007/BF02845622

It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations. Then the essential definitions and formulae from fractional calculus are summarized and their immediate use in the study of scaling in physical systems is given. This is followed by a brief summary of classical results. The main theme of the review rests on the notion of local fractional derivatives. There is a direct connection between local fractional differentiability properties and the dimensions/ local Holder exponents of nowhere differentiable functions. It is argued that local fractional derivatives provide a powerful tool to analyse the pointwise behaviour of irregular signals and functions.

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