The mean value theorem and Taylor’s theorem for fractional derivatives with Mittag–Leffler kernel

We establish analogues of the mean value theorem and Taylor’s theorem for fractional differential operators defined using a Mittag–Leffler kernel. We formulate a new model for the fractional Boussinesq equation by using this new Taylor series expansion.

Detalles Bibliográficos
Autores principales: Fernandez, Arran, Baleanu, Dumitru
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6566265/
https://www.ncbi.nlm.nih.gov/pubmed/31258614
http://dx.doi.org/10.1186/s13662-018-1543-9
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author Fernandez, Arran
Baleanu, Dumitru
author_facet Fernandez, Arran
Baleanu, Dumitru
author_sort Fernandez, Arran
collection PubMed
description We establish analogues of the mean value theorem and Taylor’s theorem for fractional differential operators defined using a Mittag–Leffler kernel. We formulate a new model for the fractional Boussinesq equation by using this new Taylor series expansion.
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spelling pubmed-65662652019-06-28 The mean value theorem and Taylor’s theorem for fractional derivatives with Mittag–Leffler kernel Fernandez, Arran Baleanu, Dumitru Adv Differ Equ Research We establish analogues of the mean value theorem and Taylor’s theorem for fractional differential operators defined using a Mittag–Leffler kernel. We formulate a new model for the fractional Boussinesq equation by using this new Taylor series expansion. Springer International Publishing 2018-03-09 2018 /pmc/articles/PMC6566265/ /pubmed/31258614 http://dx.doi.org/10.1186/s13662-018-1543-9 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
Fernandez, Arran
Baleanu, Dumitru
The mean value theorem and Taylor’s theorem for fractional derivatives with Mittag–Leffler kernel
title The mean value theorem and Taylor’s theorem for fractional derivatives with Mittag–Leffler kernel
title_full The mean value theorem and Taylor’s theorem for fractional derivatives with Mittag–Leffler kernel
title_fullStr The mean value theorem and Taylor’s theorem for fractional derivatives with Mittag–Leffler kernel
title_full_unstemmed The mean value theorem and Taylor’s theorem for fractional derivatives with Mittag–Leffler kernel
title_short The mean value theorem and Taylor’s theorem for fractional derivatives with Mittag–Leffler kernel
title_sort mean value theorem and taylor’s theorem for fractional derivatives with mittag–leffler kernel
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6566265/
https://www.ncbi.nlm.nih.gov/pubmed/31258614
http://dx.doi.org/10.1186/s13662-018-1543-9
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