Local Fractional Calculus: a Review

2013/07/02 by Kiran M. Kolwankar, Kolwankar, Kiran M. · 1 citation
Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical Physics (math-ph) #Nonlinear Differential Equations Analysis #math-ph #math.MP #nlin.CD

paper · pdf · doi:10.48550/arxiv.1307.0739

to appear in the proceedings of 'National Workshop on Fractional Calculus: Theory and Applications', University of Pune

arxiv created 2013/07/02 · openalex publication_date 2013/07/02 · arxiv updated 2018/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 applications. This involves the local fractional Taylor expansion, Leibnitz rule, chain rule, etc. Among applications we consider the local fractional diffusion equation for fractal time processes and the relation between stress and strain for fractal media. Finally, we indicate a stochastic version of local fractional differential equation.

Citations

• Studies of fractal structures and processes using methods of fractional\n calculus
• The Fractal Geometry of Nature
• Fractional Differential Equations

Cited by

• Local Fractional Calculus currently. A Mosaic of Definitions and the Quest for Unification

Related

• Studies of fractal structures and processes using methods of fractional\n calculus
• Applications of local fractional calculus to engineering in fractal time-space: Local fractional differential equations with local fractional derivative
• Local Fractional Derivatives and Fractal Functions of Several Variables
• Definition of fractal measures arising from fractional calculus
• Local Fractional Calculus currently. A Mosaic of Definitions and the Quest for Unification