Stability analysis of Hadamard and Caputo-Hadamard fractional nonlinear systems without and with delay

This paper handles with the Hadamard and the Caputo-Hadamard fractional derivative and stability of related systems without and with delay. Firstly, the derivative inequalities are obtained, which is indispensable in applying the theorems derived in this paper. Then, for systems without delay, we ge...

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Detalles Bibliográficos
Autores principales: He, Bin-Bin, Zhou, Hua-Cheng, Kou, Chun-Hai
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2022
Materias:
Original Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9663204/
https://www.ncbi.nlm.nih.gov/pubmed/36406050
http://dx.doi.org/10.1007/s13540-022-00106-3
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author He, Bin-Bin
Zhou, Hua-Cheng
Kou, Chun-Hai
author_facet He, Bin-Bin
Zhou, Hua-Cheng
Kou, Chun-Hai
author_sort He, Bin-Bin
collection PubMed
description This paper handles with the Hadamard and the Caputo-Hadamard fractional derivative and stability of related systems without and with delay. Firstly, the derivative inequalities are obtained, which is indispensable in applying the theorems derived in this paper. Then, for systems without delay, we get the stability results by using the Lyapunov direct method and for systems with delay, we explore two useful inequalities to verify the stability. Examples are presented with numerical simulations to illustrate the effectiveness of our results.
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spelling pubmed-96632042022-11-14 Stability analysis of Hadamard and Caputo-Hadamard fractional nonlinear systems without and with delay He, Bin-Bin Zhou, Hua-Cheng Kou, Chun-Hai Fract Calc Appl Anal Original Paper This paper handles with the Hadamard and the Caputo-Hadamard fractional derivative and stability of related systems without and with delay. Firstly, the derivative inequalities are obtained, which is indispensable in applying the theorems derived in this paper. Then, for systems without delay, we get the stability results by using the Lyapunov direct method and for systems with delay, we explore two useful inequalities to verify the stability. Examples are presented with numerical simulations to illustrate the effectiveness of our results. Springer International Publishing 2022-11-14 2022 /pmc/articles/PMC9663204/ /pubmed/36406050 http://dx.doi.org/10.1007/s13540-022-00106-3 Text en © Diogenes Co.Ltd 2022, Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Original Paper
He, Bin-Bin
Zhou, Hua-Cheng
Kou, Chun-Hai
Stability analysis of Hadamard and Caputo-Hadamard fractional nonlinear systems without and with delay
title Stability analysis of Hadamard and Caputo-Hadamard fractional nonlinear systems without and with delay
title_full Stability analysis of Hadamard and Caputo-Hadamard fractional nonlinear systems without and with delay
title_fullStr Stability analysis of Hadamard and Caputo-Hadamard fractional nonlinear systems without and with delay
title_full_unstemmed Stability analysis of Hadamard and Caputo-Hadamard fractional nonlinear systems without and with delay
title_short Stability analysis of Hadamard and Caputo-Hadamard fractional nonlinear systems without and with delay
title_sort stability analysis of hadamard and caputo-hadamard fractional nonlinear systems without and with delay
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9663204/
https://www.ncbi.nlm.nih.gov/pubmed/36406050
http://dx.doi.org/10.1007/s13540-022-00106-3
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