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A numerical study of fractional rheological models and fractional Newell-Whitehead-Segel equation with non-local and non-singular kernel

In the recent years, few type of fractional derivatives which have non-local and non-singular kernel are introduced. In this work, we present fractional rheological models and Newell-Whitehead-Segel equations with non-local and non-singular kernel. For solving these equations, we present a spectral...

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Autores principales: Tuan, N.H., Ganji, R.M., Jafari, H.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7462662/
http://dx.doi.org/10.1016/j.cjph.2020.08.019
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author Tuan, N.H.
Ganji, R.M.
Jafari, H.
author_facet Tuan, N.H.
Ganji, R.M.
Jafari, H.
author_sort Tuan, N.H.
collection PubMed
description In the recent years, few type of fractional derivatives which have non-local and non-singular kernel are introduced. In this work, we present fractional rheological models and Newell-Whitehead-Segel equations with non-local and non-singular kernel. For solving these equations, we present a spectral collocation method based on the shifted Legendre polynomials. To do this, we extend the unknown functions and its derivatives using the shifted Legendre basis. These expansions and the properties of the shifted Legendre polynomials along with the spectral collocation method will help us to reduce the main problem to a set of nonlinear algebraic equations. Finally, The accuracy and efficiency of the proposed method are reported by some illustrative examples.
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spelling pubmed-74626622020-09-02 A numerical study of fractional rheological models and fractional Newell-Whitehead-Segel equation with non-local and non-singular kernel Tuan, N.H. Ganji, R.M. Jafari, H. Chin J Phys Article In the recent years, few type of fractional derivatives which have non-local and non-singular kernel are introduced. In this work, we present fractional rheological models and Newell-Whitehead-Segel equations with non-local and non-singular kernel. For solving these equations, we present a spectral collocation method based on the shifted Legendre polynomials. To do this, we extend the unknown functions and its derivatives using the shifted Legendre basis. These expansions and the properties of the shifted Legendre polynomials along with the spectral collocation method will help us to reduce the main problem to a set of nonlinear algebraic equations. Finally, The accuracy and efficiency of the proposed method are reported by some illustrative examples. The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. 2020-12 2020-09-01 /pmc/articles/PMC7462662/ http://dx.doi.org/10.1016/j.cjph.2020.08.019 Text en © 2020 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. All rights reserved. Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active.
spellingShingle Article
Tuan, N.H.
Ganji, R.M.
Jafari, H.
A numerical study of fractional rheological models and fractional Newell-Whitehead-Segel equation with non-local and non-singular kernel
title A numerical study of fractional rheological models and fractional Newell-Whitehead-Segel equation with non-local and non-singular kernel
title_full A numerical study of fractional rheological models and fractional Newell-Whitehead-Segel equation with non-local and non-singular kernel
title_fullStr A numerical study of fractional rheological models and fractional Newell-Whitehead-Segel equation with non-local and non-singular kernel
title_full_unstemmed A numerical study of fractional rheological models and fractional Newell-Whitehead-Segel equation with non-local and non-singular kernel
title_short A numerical study of fractional rheological models and fractional Newell-Whitehead-Segel equation with non-local and non-singular kernel
title_sort numerical study of fractional rheological models and fractional newell-whitehead-segel equation with non-local and non-singular kernel
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7462662/
http://dx.doi.org/10.1016/j.cjph.2020.08.019
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