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Computation of solution to fractional order partial reaction diffusion equations

In this article, the considered problem of Cauchy reaction diffusion equation of fractional order is solved by using integral transform of Laplace coupled with decomposition technique due to Adomian scheme. This combination led us to a hybrid method which has been properly used to handle nonlinear a...

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Detalles Bibliográficos
Autores principales: Gul, Haji, Alrabaiah, Hussam, Ali, Sajjad, Shah, Kamal, Muhammad, Shakoor
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7474206/
https://www.ncbi.nlm.nih.gov/pubmed/32922971
http://dx.doi.org/10.1016/j.jare.2020.04.021
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author Gul, Haji
Alrabaiah, Hussam
Ali, Sajjad
Shah, Kamal
Muhammad, Shakoor
author_facet Gul, Haji
Alrabaiah, Hussam
Ali, Sajjad
Shah, Kamal
Muhammad, Shakoor
author_sort Gul, Haji
collection PubMed
description In this article, the considered problem of Cauchy reaction diffusion equation of fractional order is solved by using integral transform of Laplace coupled with decomposition technique due to Adomian scheme. This combination led us to a hybrid method which has been properly used to handle nonlinear and linear problems. The considered problem is used in modeling spatial effects in engineering, biology and ecology. The fractional derivative is considered in Caputo sense. The results are obtained in series form corresponding to the proposed problem of fractional order. To present the analytical procedure of the proposed method, some test examples are provided. An approximate solution of a fractional order diffusion equation were obtained. This solution was rapidly convergent to the exact solution with less computational cost. For the computation purposes, we used MATLAB.
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spelling pubmed-74742062020-09-11 Computation of solution to fractional order partial reaction diffusion equations Gul, Haji Alrabaiah, Hussam Ali, Sajjad Shah, Kamal Muhammad, Shakoor J Adv Res Article In this article, the considered problem of Cauchy reaction diffusion equation of fractional order is solved by using integral transform of Laplace coupled with decomposition technique due to Adomian scheme. This combination led us to a hybrid method which has been properly used to handle nonlinear and linear problems. The considered problem is used in modeling spatial effects in engineering, biology and ecology. The fractional derivative is considered in Caputo sense. The results are obtained in series form corresponding to the proposed problem of fractional order. To present the analytical procedure of the proposed method, some test examples are provided. An approximate solution of a fractional order diffusion equation were obtained. This solution was rapidly convergent to the exact solution with less computational cost. For the computation purposes, we used MATLAB. Elsevier 2020-05-15 /pmc/articles/PMC7474206/ /pubmed/32922971 http://dx.doi.org/10.1016/j.jare.2020.04.021 Text en © 2020 The Authors. Published by Elsevier B.V. on behalf of Cairo University. http://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
spellingShingle Article
Gul, Haji
Alrabaiah, Hussam
Ali, Sajjad
Shah, Kamal
Muhammad, Shakoor
Computation of solution to fractional order partial reaction diffusion equations
title Computation of solution to fractional order partial reaction diffusion equations
title_full Computation of solution to fractional order partial reaction diffusion equations
title_fullStr Computation of solution to fractional order partial reaction diffusion equations
title_full_unstemmed Computation of solution to fractional order partial reaction diffusion equations
title_short Computation of solution to fractional order partial reaction diffusion equations
title_sort computation of solution to fractional order partial reaction diffusion equations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7474206/
https://www.ncbi.nlm.nih.gov/pubmed/32922971
http://dx.doi.org/10.1016/j.jare.2020.04.021
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