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A Computational Approach for the Calculation of Temperature Distribution in Casting-Mould Heterogeneous System with Fractional Order

The purpose of this paper is to investigate the approximate solution of the casting-mould heterogeneous system with Caputo derivative under the homotopy idea. The symmetry design of the system contains the integer partial differential equations and the fractional-order partial differential equations...

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Autores principales: Luo, Xiankang, Nadeem, Muhammad, Asjad, Muhammad Imran, Abdo, Mohammed S.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9345697/
https://www.ncbi.nlm.nih.gov/pubmed/35928966
http://dx.doi.org/10.1155/2022/3648277
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author Luo, Xiankang
Nadeem, Muhammad
Asjad, Muhammad Imran
Abdo, Mohammed S.
author_facet Luo, Xiankang
Nadeem, Muhammad
Asjad, Muhammad Imran
Abdo, Mohammed S.
author_sort Luo, Xiankang
collection PubMed
description The purpose of this paper is to investigate the approximate solution of the casting-mould heterogeneous system with Caputo derivative under the homotopy idea. The symmetry design of the system contains the integer partial differential equations and the fractional-order partial differential equations. We apply Yang transform homotopy perturbation method (𝒴T-HPM) to find the approximate solution of temperature distribution in the casting-mould heterogeneous system. The 𝒴T-HPM is a combined form of Yang transform (𝒴T) and the homotopy perturbation method (HPM) using He's polynomials. Some examples are provided to demonstrate the superiority of the suggested technique. The significant findings reveal that 𝒴T-HPM minimizes the enormous without imposing any assumptions. Due to its powerful and robust support for nonlinear problems, this approach presents a remarkable appearance in the functional studies of fractal calculus.
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spelling pubmed-93456972022-08-03 A Computational Approach for the Calculation of Temperature Distribution in Casting-Mould Heterogeneous System with Fractional Order Luo, Xiankang Nadeem, Muhammad Asjad, Muhammad Imran Abdo, Mohammed S. Comput Math Methods Med Research Article The purpose of this paper is to investigate the approximate solution of the casting-mould heterogeneous system with Caputo derivative under the homotopy idea. The symmetry design of the system contains the integer partial differential equations and the fractional-order partial differential equations. We apply Yang transform homotopy perturbation method (𝒴T-HPM) to find the approximate solution of temperature distribution in the casting-mould heterogeneous system. The 𝒴T-HPM is a combined form of Yang transform (𝒴T) and the homotopy perturbation method (HPM) using He's polynomials. Some examples are provided to demonstrate the superiority of the suggested technique. The significant findings reveal that 𝒴T-HPM minimizes the enormous without imposing any assumptions. Due to its powerful and robust support for nonlinear problems, this approach presents a remarkable appearance in the functional studies of fractal calculus. Hindawi 2022-07-26 /pmc/articles/PMC9345697/ /pubmed/35928966 http://dx.doi.org/10.1155/2022/3648277 Text en Copyright © 2022 Xiankang Luo et al. https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Luo, Xiankang
Nadeem, Muhammad
Asjad, Muhammad Imran
Abdo, Mohammed S.
A Computational Approach for the Calculation of Temperature Distribution in Casting-Mould Heterogeneous System with Fractional Order
title A Computational Approach for the Calculation of Temperature Distribution in Casting-Mould Heterogeneous System with Fractional Order
title_full A Computational Approach for the Calculation of Temperature Distribution in Casting-Mould Heterogeneous System with Fractional Order
title_fullStr A Computational Approach for the Calculation of Temperature Distribution in Casting-Mould Heterogeneous System with Fractional Order
title_full_unstemmed A Computational Approach for the Calculation of Temperature Distribution in Casting-Mould Heterogeneous System with Fractional Order
title_short A Computational Approach for the Calculation of Temperature Distribution in Casting-Mould Heterogeneous System with Fractional Order
title_sort computational approach for the calculation of temperature distribution in casting-mould heterogeneous system with fractional order
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9345697/
https://www.ncbi.nlm.nih.gov/pubmed/35928966
http://dx.doi.org/10.1155/2022/3648277
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