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.

published version; modified title

References in corpus (1)

• Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus

Cited by in corpus (4)

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