Subdiffusive Reaction Model of Molecular Species in Liquid Layers: Fractional Reaction-Telegraph Approach
In recent years, different experimental works with molecular simulation techniques have been developed to study the transport of plasma-generated reactive species in liquid layers. Here, we improve the classical transport model that describes the molecular species movement in liquid layers via consi...
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doaj-7377f1daa2ce483a97120b65be85bff02021-06-30T23:10:47ZengMDPI AGFractal and Fractional2504-31102021-06-015515110.3390/fractalfract5020051Subdiffusive Reaction Model of Molecular Species in Liquid Layers: Fractional Reaction-Telegraph ApproachAshraf M. Tawfik0Mohamed Mokhtar Hefny1Theoretical Physics Research Group, Faculty of Science, Mansoura University, Mansoura 35516, EgyptEngineering Mathematics and Physics Department, Faculty of Engineering and Technology, Future University in Egypt, Cairo 11835, EgyptIn recent years, different experimental works with molecular simulation techniques have been developed to study the transport of plasma-generated reactive species in liquid layers. Here, we improve the classical transport model that describes the molecular species movement in liquid layers via considering the fractional reaction–telegraph equation. We have considered the fractional equation to describe a non-Brownian motion of molecular species in a liquid layer, which have different diffusivities. The analytical solution of the fractional reaction–telegraph equation, which is defined in terms of the Caputo fractional derivative, is obtained by using the Laplace–Fourier technique. The profiles of species density with the mean square displacement are discussed in each case for different values of the time-fractional order and relaxation time.https://www.mdpi.com/2504-3110/5/2/51anomalous diffusionfractional calculuscold atmospheric plasmaplasma with liquids |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Ashraf M. Tawfik Mohamed Mokhtar Hefny |
spellingShingle |
Ashraf M. Tawfik Mohamed Mokhtar Hefny Subdiffusive Reaction Model of Molecular Species in Liquid Layers: Fractional Reaction-Telegraph Approach Fractal and Fractional anomalous diffusion fractional calculus cold atmospheric plasma plasma with liquids |
author_facet |
Ashraf M. Tawfik Mohamed Mokhtar Hefny |
author_sort |
Ashraf M. Tawfik |
title |
Subdiffusive Reaction Model of Molecular Species in Liquid Layers: Fractional Reaction-Telegraph Approach |
title_short |
Subdiffusive Reaction Model of Molecular Species in Liquid Layers: Fractional Reaction-Telegraph Approach |
title_full |
Subdiffusive Reaction Model of Molecular Species in Liquid Layers: Fractional Reaction-Telegraph Approach |
title_fullStr |
Subdiffusive Reaction Model of Molecular Species in Liquid Layers: Fractional Reaction-Telegraph Approach |
title_full_unstemmed |
Subdiffusive Reaction Model of Molecular Species in Liquid Layers: Fractional Reaction-Telegraph Approach |
title_sort |
subdiffusive reaction model of molecular species in liquid layers: fractional reaction-telegraph approach |
publisher |
MDPI AG |
series |
Fractal and Fractional |
issn |
2504-3110 |
publishDate |
2021-06-01 |
description |
In recent years, different experimental works with molecular simulation techniques have been developed to study the transport of plasma-generated reactive species in liquid layers. Here, we improve the classical transport model that describes the molecular species movement in liquid layers via considering the fractional reaction–telegraph equation. We have considered the fractional equation to describe a non-Brownian motion of molecular species in a liquid layer, which have different diffusivities. The analytical solution of the fractional reaction–telegraph equation, which is defined in terms of the Caputo fractional derivative, is obtained by using the Laplace–Fourier technique. The profiles of species density with the mean square displacement are discussed in each case for different values of the time-fractional order and relaxation time. |
topic |
anomalous diffusion fractional calculus cold atmospheric plasma plasma with liquids |
url |
https://www.mdpi.com/2504-3110/5/2/51 |
work_keys_str_mv |
AT ashrafmtawfik subdiffusivereactionmodelofmolecularspeciesinliquidlayersfractionalreactiontelegraphapproach AT mohamedmokhtarhefny subdiffusivereactionmodelofmolecularspeciesinliquidlayersfractionalreactiontelegraphapproach |
_version_ |
1721352008248590336 |