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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...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Hindawi
2022
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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. |
format | Online Article Text |
id | pubmed-9345697 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Hindawi |
record_format | MEDLINE/PubMed |
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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