Diffusion on middle-ξ Cantor sets
Published version
Peer-reviewed
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Repository DOI
Change log
Authors
Golmankhaneh, Alireza K
Fernandez, Arran https://orcid.org/0000-0002-1491-1820
Golmankhaneh, Ali K
Baleanu, Dumitru
Abstract
In this paper, we study C^ζ -calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions. Functions with fractal support are not differentiable or integrable in terms of standard calculus, so we must involve local fractional derivatives. We have generalized the C^ζ -calculus on the generalized Cantor sets known as middle-ξ Cantor sets. We have suggested a calculus on the middle-ξ Cantor sets for different values of ξ with 0 < ξ < 1. Differential equations on the middle-ξ Cantor sets have been solved, and we have presented the results using illustrative examples. The conditions for super-, normal, and sub-diffusion on fractal sets are given.
Description
Keywords
Hausdorff dimension, middle-ξ Cantor sets, staircase function, Cζ-calculus, diffusion on fractal, random walk
Journal Title
Entropy
Conference Name
Journal ISSN
1099-4300
1099-4300
1099-4300
Volume Title
20
Publisher
MDPI AG
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Sponsorship
EPSRC (1479943)