Simple Fractal Calculus from Fractal Arithmetic

Diederik Aerts; Marek Czachor; Maciej Kuna

doi:10.1016/s0034-4877(18)30053-3

Simple Fractal Calculus from Fractal Arithmetic

Abstract

Non-Newtonian calculus that starts with elementary non-Diophantine arithmetic operations of a Burgin type is applicable to all fractals whose cardinality is continuum. The resulting definitions of derivatives and integrals are simpler from what one finds in the more traditional literature of the subject, and they often work in the cases where the standard methods fail. As an illustration, we perform a Fourier transform of a real-valued function with Sierpiński-set domain. The resulting formalism is as simple as the usual undergraduate calculus.

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DOI:: Digital Object Identifier (open in new tab) 10.1016/S0034-4877(18)30053-3
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Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: REPORTS ON MATHEMATICAL PHYSICS no. 81, edition 3, pages 359 - 372,
ISSN: 0034-4877
Language:: English
Publication year:: 2018
Bibliographic description:: Aerts, D., Czachor M., Kuna M.: Simple Fractal Calculus from Fractal Arithmetic// REPORTS ON MATHEMATICAL PHYSICS. -Vol. 81, iss. 3 (2018), s.359-372
DOI:: Digital Object Identifier (open in new tab) 10.1016/s0034-4877(18)30053-3
Verified by:: Gdańsk University of Technology