title: Fractional differentiability of nowhere differentiable functions and dimensions.
abstract: Weierstrass's everywhere continuous but nowhere differentiable function is shown to be locally continuously fractionally differentiable everywhere for all orders below the "critical order" 2-s and not so for orders between 2-s and 1, where s, 1<s<2 is the box dimension of the graph of the function. This observation is consolidated in the general result showing a direct connection between local fractional differentiability and the box dimension/local Holder exponent. Levy index for one dimensional Levy flights is shown to be the critical order of its characteristic function. Local fractional derivatives of multifractal signals (non-random functions) are shown to provide the local Holder exponent. It is argued that Local fractional derivatives provide a powerful tool to analyze pointwise behavior of irregular signals. (c) 1996 American Institute of Physics.
authors.affiliation: Department of Physics, University of Pune, Pune 411 007, India.
authors.forename: Kiran M.
authors.initials: KM
authors.lastname: Kolwankar
authors.forename: Anil D.
authors.initials: AD
authors.lastname: Gangal