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...

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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
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description	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
doi_str_mv	10.1515/fca-2020-0066
format	Article
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subjects	28A80 Abstract Harmonic Analysis Analysis Fractals fractional calculus Functional Analysis Grünwald-Letnikov Integral Transforms iterated function system Mathematics Operational Calculus Primary 26A33 Research Paper
title	Fractional Fractals
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