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Fractional differentiability of nowhere differentiable functions and dimensions.

- K. M. Kolwankar, A. D. Gangal
- MathematicsChaos
- 24 September 1996

TLDR

Local Fractional Fokker-Planck Equation

- K. M. Kolwankar, A. D. Gangal
- Mathematics
- 12 January 1998

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… Expand

Hölder exponents of irregular signals and local fractional derivatives

- K. M. Kolwankar, A. D. Gangal
- Mathematics
- 9 November 1997

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… Expand

Local Fractional Calculus: a Calculus for Fractal Space-Time

- K. M. Kolwankar, A. D. Gangal
- Mathematics
- 1999

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… Expand

A Time Domain Characterization of the Fine Local Regularity of Functions

- K. M. Kolwankar, J. L. Véhel
- Mathematics
- 1 July 2002

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… Expand

Local Fractional Derivatives and Fractal Functions of Several Variables

- K. M. Kolwankar, A. D. Gangal
- Mathematics
- 10 January 1998

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… Expand

Studies of fractal structures and processes using methods of fractional calculus

- K. M. Kolwankar
- Mathematics
- 4 November 1998

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… Expand

Calculation of the tensile and flexural strength of disordered materials using fractional calculus

- A. Carpinteri, P. Cornetti, K. M. Kolwankar
- Materials Science
- 1 July 2004

MEASURING FUNCTIONS SMOOTHNESS WITH LOCAL FRACTIONAL DERIVATIVES

- K. M. Kolwankar, J. L. Vhel
- Mathematics
- 2001

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… Expand

Local Fractional Calculus: a Review

- K. M. Kolwankar
- Mathematics
- 2 July 2013

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… Expand

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