Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (1)

Search Parameters:
Keywords = middle-ξ Cantor sets

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
13 pages, 472 KB  
Article
Diffusion on Middle-ξ Cantor Sets
by Alireza Khalili Golmankhaneh, Arran Fernandez, Ali Khalili Golmankhaneh and Dumitru Baleanu
Entropy 2018, 20(7), 504; https://doi.org/10.3390/e20070504 - 2 Jul 2018
Cited by 50 | Viewed by 5507
Abstract
In this paper, we study Cζ-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 [...] Read more.
In this paper, we study Cζ-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 Cζ-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. Full article
(This article belongs to the Special Issue Power Law Behaviour in Complex Systems)
►▼ Show Figures

Figure 1

Back to TopTop