$Optimal solution of the fractional order breast cancer competition model$
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Optimal solution of the fractional order breast cancer competition model

Abstract In this article, a fractional order breast cancer competition model (F-BCCM) under the Caputo fractional derivative is analyzed. A new set of basis functions, namely the generalized shifted Legendre polynomials, is proposed to deal with the solutions of F-BCCM. The F-BCCM describes the dyna...

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Autores principales:	H. Hassani, J. A. Tenreiro Machado, Z. Avazzadeh, E. Safari, S. Mehrabi
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/3ffb246adee24e89b2858c38be54519a
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spelling	oai:doaj.org-article:3ffb246adee24e89b2858c38be54519a2021-12-02T16:35:18ZOptimal solution of the fractional order breast cancer competition model10.1038/s41598-021-94875-12045-2322https://doaj.org/article/3ffb246adee24e89b2858c38be54519a2021-08-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-94875-1https://doaj.org/toc/2045-2322Abstract In this article, a fractional order breast cancer competition model (F-BCCM) under the Caputo fractional derivative is analyzed. A new set of basis functions, namely the generalized shifted Legendre polynomials, is proposed to deal with the solutions of F-BCCM. The F-BCCM describes the dynamics involving a variety of cancer factors, such as the stem, tumor and healthy cells, as well as the effects of excess estrogen and the body’s natural immune response on the cell populations. After combining the operational matrices with the Lagrange multipliers technique we obtain an optimization method for solving the F-BCCM whose convergence is investigated. Several examples show that a few number of basis functions lead to the satisfactory results. In fact, numerical experiments not only confirm the accuracy but also the practicability and computational efficiency of the devised technique.H. HassaniJ. A. Tenreiro MachadoZ. AvazzadehE. SafariS. MehrabiNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-15 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q H. Hassani J. A. Tenreiro Machado Z. Avazzadeh E. Safari S. Mehrabi Optimal solution of the fractional order breast cancer competition model
description	Abstract In this article, a fractional order breast cancer competition model (F-BCCM) under the Caputo fractional derivative is analyzed. A new set of basis functions, namely the generalized shifted Legendre polynomials, is proposed to deal with the solutions of F-BCCM. The F-BCCM describes the dynamics involving a variety of cancer factors, such as the stem, tumor and healthy cells, as well as the effects of excess estrogen and the body’s natural immune response on the cell populations. After combining the operational matrices with the Lagrange multipliers technique we obtain an optimization method for solving the F-BCCM whose convergence is investigated. Several examples show that a few number of basis functions lead to the satisfactory results. In fact, numerical experiments not only confirm the accuracy but also the practicability and computational efficiency of the devised technique.
format	article
author	H. Hassani J. A. Tenreiro Machado Z. Avazzadeh E. Safari S. Mehrabi
author_facet	H. Hassani J. A. Tenreiro Machado Z. Avazzadeh E. Safari S. Mehrabi
author_sort	H. Hassani
title	Optimal solution of the fractional order breast cancer competition model
title_short	Optimal solution of the fractional order breast cancer competition model
title_full	Optimal solution of the fractional order breast cancer competition model
title_fullStr	Optimal solution of the fractional order breast cancer competition model
title_full_unstemmed	Optimal solution of the fractional order breast cancer competition model
title_sort	optimal solution of the fractional order breast cancer competition model
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/3ffb246adee24e89b2858c38be54519a
work_keys_str_mv	AT hhassani optimalsolutionofthefractionalorderbreastcancercompetitionmodel AT jatenreiromachado optimalsolutionofthefractionalorderbreastcancercompetitionmodel AT zavazzadeh optimalsolutionofthefractionalorderbreastcancercompetitionmodel AT esafari optimalsolutionofthefractionalorderbreastcancercompetitionmodel AT smehrabi optimalsolutionofthefractionalorderbreastcancercompetitionmodel
_version_	1718383685812617216

Optimal solution of the fractional order breast cancer competition model

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