Search
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.
Citations
-
6
CrossRef
-
0
Web of Science
-
7
Scopus
Authors (3)
-
Diederik Aerts
- VUB
-
Maciej Kuna
- UG
Cite as
Full text
download paper
downloaded 42 times
- Publication version
- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/S0034-4877(18)30053-3
- License
-
open in new tab
Keywords
Details
- 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
seen 155 times