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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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Authors (3)
-
Diederik Aerts
- VUB
-
Maciej Kuna
- UG
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- Accepted or Published Version
- 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
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