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

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          Abstract

          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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          The random walk's guide to anomalous diffusion: a fractional dynamics approach

          Ralf Metzler, Joseph Klafter (2000)
          Article 0 comments Cited 302 times – based on 0 reviews     Review now
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            Mittag–Leffler stability of fractional order nonlinear dynamic systems

            Yan. Li, YangQuan Chen, Igor Podlubny (2009)
            Article 0 comments Cited 169 times – based on 0 reviews     Review now
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              Applications of Fractional Calculus in Physics

              R. Hilfer (2000)
              Book 0 comments Cited 167 times – based on 0 reviews
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                Author and article information

                Contributors
                Bin-Bin He: hebinbin45@126.com
                Hua-Cheng Zhou:
                ORCID: http://orcid.org/0000-0001-6856-2358
                hczhou@amss.ac.cn
                Chun-Hai Kou: kouchunhai@dhu.edu.cn
                Journal
                Journal ID (nlm-ta): Fract Calc Appl Anal
                Journal ID (iso-abbrev): Fract Calc Appl Anal
                Title: Fractional Calculus & Applied Analysis
                Publisher: Springer International Publishing (Cham )
                ISSN (Print): 1311-0454
                ISSN (Electronic): 1314-2224
                Publication date (Electronic): 14 November 2022
                Pages: 1-26
                Affiliations
                [1 ]GRID grid.469325.f, ISNI 0000 0004 1761 325X, College of Science, , Zhejiang University of Technology, ; Hangzhou, 310023 Zhejiang People’s Republic of China
                [2 ]GRID grid.216417.7, ISNI 0000 0001 0379 7164, School of Mathematics and Statistics, HNP-LAMA, , Central South University, ; Changsha, 410083 Hunan People’s Republic of China
                [3 ]GRID grid.255169.c, ISNI 0000 0000 9141 4786, Department of Applied Mathematics, , Donghua University, ; Shanghai, 201620 People’s Republic of China
                Author information
                http://orcid.org/0000-0001-6856-2358
                Article
                Publisher ID: 106
                DOI: 10.1007/s13540-022-00106-3
                PMC ID: 9663204
                SO-VID: fb67f3db-abc2-4364-b35f-bb93c1c14960
                Copyright © © 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.
                License:

                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.

                History
                Date received : 12 May 2022
                Date revision received : 2 November 2022
                Date accepted : 3 November 2022
                Funding
                Funded by: FundRef http://dx.doi.org/10.13039/501100004735, Natural Science Foundation of Hunan Province;
                Award ID: 2021JJ20081
                Award Recipient :
                Funded by: FundRef http://dx.doi.org/10.13039/501100001809, National Natural Science Foundation of China;
                Award ID: 62173348
                Award Recipient :
                Categories
                Subject: Original Paper

                Keywords: hadamard system,caputo-hadamard system,stability,fractional lyapunov method,fractional halanay inequality,26a33,34a08,37b25,34k37
                Data availability:
                Keywords: hadamard system, caputo-hadamard system, stability, fractional lyapunov method, fractional halanay inequality, 26a33, 34a08, 37b25, 34k37

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