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Fractional differentiability of nowhere differentiable functions and dimensions.
TLDR
It is argued that Local fractional derivatives provide a powerful tool to analyze pointwise behavior of irregular signals to show a direct connection between local fractional differentiability and the box dimension/local Holder exponent.
Local Fractional Fokker-Planck Equation
We propose a new class of differential equations, which we call local fractional differential equations. They involve local fractional derivatives and appear to be suitable to deal with phenomena
Hölder exponents of irregular signals and local fractional derivatives
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
Local Fractional Calculus: a Calculus for Fractal Space-Time
Recently, new notions such as local fractional derivatives and local fractional differential equations were introduced. Here we argue that these developments provide a possible calculus to deal with
A Time Domain Characterization of the Fine Local Regularity of Functions
We define new functional spaces designed to measure the fine local regularity of functions. In contrast with classical approaches based on, e. g., Littlewood-Paley or wavelet analysis, these spaces
Local Fractional Derivatives and Fractal Functions of Several Variables
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
Studies of fractal structures and processes using methods of fractional calculus
The thesis deals with applications of fractional calculus to fractals. It introduces the notion of local fractional derivative (LFD). Fractal and multifractal functions have been studied in the
MEASURING FUNCTIONS SMOOTHNESS WITH LOCAL FRACTIONAL DERIVATIVES
We study a notion of local fractional differentiation, obtained by localizing the classical fractional derivative. We show that it is strongly related with the local Holder exponent, and give an
Local Fractional Calculus: a Review
The purpose of this article is to review the developments related to the notion of local fractional derivative introduced in 1996. We consider its definition, properties, implications and possible
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