Work

Diffusion on Middle-ξ Cantor Sets

Year: 2018

Type: article

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 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.

Source: Entropy

DOI: 10.3390/e20070504

Authors: Alireza Khalili Golmankhaneh, Alireza Khalili Golmankhaneh, Arran Fernandez, Ali Khalili Golmankhaneh, Ali Khalili Golmankhaneh, Dumitru Baleanu

Institutions: Islamic Azad University of Urmia, University of Cambridge, Çankaya University, Institute of Space Science - INFLPR Subsidiary

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,278

Funder: Engineering and Physical Sciences Research Council

Award: G8275244772

OpenAlex ID: W2803821225

FWCI: 3.3

Cites: 43

Cited by: 47

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