Fractional Herglotz variational problems with Atangana–Baleanu fractional derivatives

The purpose of this paper is to solve fractional calculus of variational Herglotz problem depending on an Atangana–Baleanu fractional derivative. Since the new Atangana–Baleanu fractional derivative is non-singular and non-local, the Euler–Lagrange equations are proposed for the problems of Herglotz...

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Detalles Bibliográficos
Autores principales: Zhang, Jianke, Yin, Luyang, Zhou, Chang
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5816829/
https://www.ncbi.nlm.nih.gov/pubmed/29497264
http://dx.doi.org/10.1186/s13660-018-1635-9
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author Zhang, Jianke
Yin, Luyang
Zhou, Chang
author_facet Zhang, Jianke
Yin, Luyang
Zhou, Chang
author_sort Zhang, Jianke
collection PubMed
description The purpose of this paper is to solve fractional calculus of variational Herglotz problem depending on an Atangana–Baleanu fractional derivative. Since the new Atangana–Baleanu fractional derivative is non-singular and non-local, the Euler–Lagrange equations are proposed for the problems of Herglotz. Fractional variational Herglotz problems of variable order are considered and two cases are shown. The Noether-type theorem with this new fractional derivative is proved. Several typical examples of the results of this paper are expressed in this paper.
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spelling pubmed-58168292018-02-27 Fractional Herglotz variational problems with Atangana–Baleanu fractional derivatives Zhang, Jianke Yin, Luyang Zhou, Chang J Inequal Appl Research The purpose of this paper is to solve fractional calculus of variational Herglotz problem depending on an Atangana–Baleanu fractional derivative. Since the new Atangana–Baleanu fractional derivative is non-singular and non-local, the Euler–Lagrange equations are proposed for the problems of Herglotz. Fractional variational Herglotz problems of variable order are considered and two cases are shown. The Noether-type theorem with this new fractional derivative is proved. Several typical examples of the results of this paper are expressed in this paper. Springer International Publishing 2018-02-17 2018 /pmc/articles/PMC5816829/ /pubmed/29497264 http://dx.doi.org/10.1186/s13660-018-1635-9 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Zhang, Jianke
Yin, Luyang
Zhou, Chang
Fractional Herglotz variational problems with Atangana–Baleanu fractional derivatives
title Fractional Herglotz variational problems with Atangana–Baleanu fractional derivatives
title_full Fractional Herglotz variational problems with Atangana–Baleanu fractional derivatives
title_fullStr Fractional Herglotz variational problems with Atangana–Baleanu fractional derivatives
title_full_unstemmed Fractional Herglotz variational problems with Atangana–Baleanu fractional derivatives
title_short Fractional Herglotz variational problems with Atangana–Baleanu fractional derivatives
title_sort fractional herglotz variational problems with atangana–baleanu fractional derivatives
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5816829/
https://www.ncbi.nlm.nih.gov/pubmed/29497264
http://dx.doi.org/10.1186/s13660-018-1635-9
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AT yinluyang fractionalherglotzvariationalproblemswithatanganabaleanufractionalderivatives
AT zhouchang fractionalherglotzvariationalproblemswithatanganabaleanufractionalderivatives

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