Fractional Fractals

Fractional Fractals

This paper introduces the notion of “fractional fractals”. The main idea is to establish a connection between the classical iterated function system and the first order truncation of the Grndwald-Letnikov fractional derivative. This allows us to consider higher order truncations, and also to study t...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Fractional calculus & applied analysis 2020-10, Vol.23 (5), p.1329-1348
Hauptverfasser: Tenreiro Machado, J. A., Cao Labora, Daniel
Format: Artikel
Sprache:eng
Schlagworte:
28A80
Abstract Harmonic Analysis
Analysis
Fractals
fractional calculus
Functional Analysis
Grünwald-Letnikov
Integral Transforms
iterated function system
Mathematics
Operational Calculus
Primary 26A33
Research Paper
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:This paper introduces the notion of “fractional fractals”. The main idea is to establish a connection between the classical iterated function system and the first order truncation of the Grndwald-Letnikov fractional derivative. This allows us to consider higher order truncations, and also to study the limit sets for these higher order systems. We prove several results involving the existence and dimension of such limit sets, that will be called “fractional fractals”. Some numerical calculations and representations illustrate relevant examples. MSC 2010 : Primary 26A33, 28A80
ISSN:1311-0454
1314-2224
DOI:10.1515/fca-2020-0066