Diffusion on Middle-

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

Abstract read

In one paragraph

Article in Entropy (Basel, Switzerland), 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.

0numbers the graph read from it

0cells of the map it votes in

1citing papers in PubMed

–field-weighted citation impact

1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

The trial behind it

Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.

Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.

3 · Its place in the literature

Who cites it

1 citing paper in PubMed.

Power Law Behaviour in Complex Systems.Entropy (Basel, Switzerland) · 2018
Article

4 · The record

Corrections and comments

PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

4 authors.

Alireza Khalili GolmankhanehDepartment of Physics, Urmia Branch, Islamic Azad University, Urmia, Iran.ORCID 0000-0002-5008-0163

Arran FernandezDepartment of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK.ORCID 0000-0002-1491-1820

Ali Khalili GolmankhanehYoung Researchers and Elite Club, Urmia Branch, Islamic Azad University, Urmia, Iran.

Dumitru BaleanuDepartment of Mathematics, Cankaya University, Ankara 06530, Turkey.ORCID 0000-0002-0286-7244

Funding

No grant is acknowledged in the PubMed record.

6 · The paper itself

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.

Indexed as

Cζ-calculusdiffusion on fractalHausdorff dimensionmiddle-ξ Cantor setsrandom walkstaircase function

Identifiers

PMID33265594

DOI10.3390/e20070504

PMCPMC7513040

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.