Document Zbl 1510.34016

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Nonlinear Sci. Numer. Simul.</a> <a href="/?q=in%3A454310" title="Articles in this Issue">69, 398-415 (2019)</a>. </div> <div class="abstract">Summary: This paper investigates the asymptotic stability of equilibrium points of multivariable fractional order systems where its state equations contain different fractional orders which lie between 0 and 1. First, a fractional comparison principle is presented. Then, some elementary comparison results for linear fractional order systems of different fractional orders are developed. Based on continuously differentiable quadratic function and comparison results, new sufficient conditions are established for the asymptotic stability of linear and nonlinear multivariable fractional order systems. Finally, a few illustrative examples are presented.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7263966">Cited in <strong>25</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A34A08" title="MSC2020">34A08</a> </td> <td class="space"> Fractional ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34D20" title="MSC2020">34D20</a> </td> <td class="space"> Stability of solutions to ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A26A33" title="MSC2020">26A33</a> </td> <td class="space"> Fractional derivatives and integrals </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34C05" title="MSC2020">34C05</a> </td> <td class="space"> Topological structure of integral curves, singular points, limit cycles of ordinary differential equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Amultivariable">multivariable</a>; <a href="/?q=ut%3Afractional+order+system">fractional order system</a>; <a href="/?q=ut%3Afractional+comparison+principle">fractional comparison principle</a>; <a href="/?q=ut%3Aasymptotic+stability">asymptotic stability</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1510.34016" data-ciurl="/ci/07263966" data-biburl="/bibtex/07263966.bib" data-amsurl="/amsrefs/07263966.bib" data-xmlurl="/xml/07263966.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07263966.pdf" title="Zbl 1510.34016 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.cnsns.2018.09.016" aria-label="DOI for “Fractional comparison method and asymptotic stability results for multivariable fractional order systems”" title="10.1016/j.cnsns.2018.09.016">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Matignon, D., Stability results of fractional differential equations with applications to control processing, Proceeding of IMACS, IEEE-SMC, Lille, France, 963-968 (1996)</td> </tr><tr> <td>[2]</td> <td class="space">Podlubny, I., Fractional differential equations (1999), Academic Press: Academic Press San Diego · <a href="/0918.34010" class="nowrap">Zbl 0918.34010</a></td> </tr><tr> <td>[3]</td> <td class="space">Khalil, H. 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K.; Banerjee, S., Asymptotic stability and stabilization of a class of nonautonomous fractional order systems, Nonlinear Dyn, 85, 167-177 (2016) · <a href="/1349.34010" class="nowrap">Zbl 1349.34010</a></td> </tr><tr> <td>[22]</td> <td class="space">Azar, A. T.; Vaidyanathan, S.; Ouannas, A., Fractional order control and synchronization of chaotic systems (2017), Springer</td> </tr><tr> <td>[23]</td> <td class="space">Lenka, B. K.; Banerjee, S., Sufficient conditions for asymptotic stability and stabilization of autonomous fractional order systems, Commun Nonlinear Sci Numer Simul, 56, 365-379 (2018) · <a href="/1510.34017" class="nowrap">Zbl 1510.34017</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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