Existence theory and numerical analysis of three species prey–predator model under Mittag-Leffler power law

In this manuscript, the fractional Atangana–Baleanu–Caputo model of prey and predator is studied theoretically and numerically. The existence and Ulam–Hyers stability results are obtained by applying fixed point theory and nonlinear analysis. The approximation solutions for the considered model are...

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Autores principales: Abdo, Mohammed S., Panchal, Satish K., Shah, Kamal, Abdeljawad, Thabet
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2020
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7251561/
https://www.ncbi.nlm.nih.gov/pubmed/32501396
http://dx.doi.org/10.1186/s13662-020-02709-7
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author Abdo, Mohammed S.
Panchal, Satish K.
Shah, Kamal
Abdeljawad, Thabet
author_facet Abdo, Mohammed S.
Panchal, Satish K.
Shah, Kamal
Abdeljawad, Thabet
author_sort Abdo, Mohammed S.
collection PubMed
description In this manuscript, the fractional Atangana–Baleanu–Caputo model of prey and predator is studied theoretically and numerically. The existence and Ulam–Hyers stability results are obtained by applying fixed point theory and nonlinear analysis. The approximation solutions for the considered model are discussed via the fractional Adams Bashforth method. Moreover, the behavior of the solution to the given model is explained by graphical representations through the numerical simulations. The obtained results play an important role in developing the theory of fractional analytical dynamic of many biological systems.
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spelling pubmed-72515612020-05-27 Existence theory and numerical analysis of three species prey–predator model under Mittag-Leffler power law Abdo, Mohammed S. Panchal, Satish K. Shah, Kamal Abdeljawad, Thabet Adv Differ Equ Research In this manuscript, the fractional Atangana–Baleanu–Caputo model of prey and predator is studied theoretically and numerically. The existence and Ulam–Hyers stability results are obtained by applying fixed point theory and nonlinear analysis. The approximation solutions for the considered model are discussed via the fractional Adams Bashforth method. Moreover, the behavior of the solution to the given model is explained by graphical representations through the numerical simulations. The obtained results play an important role in developing the theory of fractional analytical dynamic of many biological systems. Springer International Publishing 2020-05-27 2020 /pmc/articles/PMC7251561/ /pubmed/32501396 http://dx.doi.org/10.1186/s13662-020-02709-7 Text en © The Author(s) 2020 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Research
Abdo, Mohammed S.
Panchal, Satish K.
Shah, Kamal
Abdeljawad, Thabet
Existence theory and numerical analysis of three species prey–predator model under Mittag-Leffler power law
title Existence theory and numerical analysis of three species prey–predator model under Mittag-Leffler power law
title_full Existence theory and numerical analysis of three species prey–predator model under Mittag-Leffler power law
title_fullStr Existence theory and numerical analysis of three species prey–predator model under Mittag-Leffler power law
title_full_unstemmed Existence theory and numerical analysis of three species prey–predator model under Mittag-Leffler power law
title_short Existence theory and numerical analysis of three species prey–predator model under Mittag-Leffler power law
title_sort existence theory and numerical analysis of three species prey–predator model under mittag-leffler power law
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7251561/
https://www.ncbi.nlm.nih.gov/pubmed/32501396
http://dx.doi.org/10.1186/s13662-020-02709-7
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