Diffusion on Middle- Cantor Sets
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Date
2018
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MDPI
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Abstract
In this paper, we study C-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-calculus on the generalized Cantor sets known as middle- Cantor sets. We have suggested a calculus on the middle- Cantor sets for different values of with 0<<1. Differential equations on the middle- 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.
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Keywords
Hausdorff Dimension, Middle- Cantor Sets, Staircase Function, C-Calculus, Diffusion on Fractal, Random Walk
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Citation
Golmankhaneh, Alireza Khalili; Fernandez, Arran; Golmankhaneh, Ali Khalili; et al. (2018). Diffusion on Middle- Cantor Sets, Entropy, 20(7).
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Source
Entropy
Volume
20
Issue
7