Stability analysis for a class of implicit fractional differential equations involving Atangana–Baleanu fractional derivative

Some fundamental conditions and hypotheses are established to ensure the existence, uniqueness, and stability to a class of implicit boundary value problems (BVPs) with Atangana–Baleanu–Caputo type derivative and integral. The required results are established by utilizing the Banach contraction mapp...

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Autores principales: Asma, Shabbir, Sana, Shah, Kamal, Abdeljawad, Thabet
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2021
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8383261/
https://www.ncbi.nlm.nih.gov/pubmed/34456987
http://dx.doi.org/10.1186/s13662-021-03551-1
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author Asma
Shabbir, Sana
Shah, Kamal
Abdeljawad, Thabet
author_facet Asma
Shabbir, Sana
Shah, Kamal
Abdeljawad, Thabet
author_sort Asma
collection PubMed
description Some fundamental conditions and hypotheses are established to ensure the existence, uniqueness, and stability to a class of implicit boundary value problems (BVPs) with Atangana–Baleanu–Caputo type derivative and integral. The required results are established by utilizing the Banach contraction mapping principle and fixed point theorem of Krasnoselskii. In addition, various types of stability results including Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam–Rassias, and generalized Hyers–Ulam–Rassias stability are formulated for the problem under consideration. Pertinent examples are given to justify the results we obtain.
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spelling pubmed-83832612021-08-24 Stability analysis for a class of implicit fractional differential equations involving Atangana–Baleanu fractional derivative Asma Shabbir, Sana Shah, Kamal Abdeljawad, Thabet Adv Differ Equ Research Some fundamental conditions and hypotheses are established to ensure the existence, uniqueness, and stability to a class of implicit boundary value problems (BVPs) with Atangana–Baleanu–Caputo type derivative and integral. The required results are established by utilizing the Banach contraction mapping principle and fixed point theorem of Krasnoselskii. In addition, various types of stability results including Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam–Rassias, and generalized Hyers–Ulam–Rassias stability are formulated for the problem under consideration. Pertinent examples are given to justify the results we obtain. Springer International Publishing 2021-08-24 2021 /pmc/articles/PMC8383261/ /pubmed/34456987 http://dx.doi.org/10.1186/s13662-021-03551-1 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/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/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Research
Asma
Shabbir, Sana
Shah, Kamal
Abdeljawad, Thabet
Stability analysis for a class of implicit fractional differential equations involving Atangana–Baleanu fractional derivative
title Stability analysis for a class of implicit fractional differential equations involving Atangana–Baleanu fractional derivative
title_full Stability analysis for a class of implicit fractional differential equations involving Atangana–Baleanu fractional derivative
title_fullStr Stability analysis for a class of implicit fractional differential equations involving Atangana–Baleanu fractional derivative
title_full_unstemmed Stability analysis for a class of implicit fractional differential equations involving Atangana–Baleanu fractional derivative
title_short Stability analysis for a class of implicit fractional differential equations involving Atangana–Baleanu fractional derivative
title_sort stability analysis for a class of implicit fractional differential equations involving atangana–baleanu fractional derivative
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8383261/
https://www.ncbi.nlm.nih.gov/pubmed/34456987
http://dx.doi.org/10.1186/s13662-021-03551-1
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