# Roman Pasechnik

Senior lecturer

## Fractal Derivatives, Fractional Derivatives and q-Deformed Calculus

Author

## Summary, in English

This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff’s concepts of fractional dimension geometry. The paper distinguishes between the derivative of a function on a fractal domain and the derivative of a fractal function, where the image is a fractal space. Different continuous approximations for the fractal derivative are discussed, and it is shown that the q-calculus derivative is a continuous approximation of the fractal derivative of a fractal function. A similar version can be obtained for the derivative of a function on a fractal space. Caputo’s derivative is also proportional to a continuous approximation of the fractal derivative, and the corresponding approximation of the derivative of a fractional function leads to a Caputo-like derivative. This work has implications for studies of fractional differential equations, anomalous diffusion, information and epidemic spread in fractal systems, and fractal geometry.

Department/s

- Department of Physics
- Lund University

Publishing year

2023-07

Language

English

Publication/Series

Entropy

Volume

25

Issue

7

Document type

Journal article

Publisher

MDPI AG

Topic

- Other Physics Topics
- Other Mathematics

Keywords

- fractal derivatives
- fractional derivatives
- fractional differential equations
- nonextensive statistics
- q-calculus

Status

Published

ISBN/ISSN/Other

- ISSN: 1099-4300