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Appl. Anal.</a> <a href="/?q=in%3A418814" title="Articles in this Issue">2014, Article ID 631419, 6 p. (2014)</a>. </div> <div class="abstract">Summary: We introduce the notion of \(h\)-stability for fractional differential systems. Then we investigate the boundedness and \(h\)-stability of solutions of Caputo fractional differential systems by using fractional comparison principle and fractional Lyapunov direct method. Furthermore, we give examples to illustrate our results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7022779">Cited in <strong>38</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%3A34A08" title="MSC2020">34A08</a> </td> <td class="space"> Fractional ordinary differential equations </td> </tr></table> </div> <!-- Modal used to show zbmath metadata in different output formats--> <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;"> <!-- alert for connection errors etc --> </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"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1474.34382" data-ciurl="/ci/07022779" data-biburl="/bibtex/07022779.bib" data-amsurl="/amsrefs/07022779.bib" data-xmlurl="/xml/07022779.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07022779.pdf" title="Zbl 1474.34382 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/10.1155/2014/631419" aria-label="DOI for “Stability for Caputo fractional differential systems”" title="10.1155/2014/631419">DOI</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/3.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Lakshmikantham, V.; Vatsala, A. S., Theory of fractional differential inequalities and applications, Communications in Applied Analysis, 11, 3-4, 395-402 (2007) · <a href="/1159.34006" class="nowrap">Zbl 1159.34006</a></td> </tr><tr> <td>[2]</td> <td class="space">Lakshmikantham, V.; Vatsala, A. S., Basic theory of fractional differential equations, Nonlinear Analysis: Theory, Methods & Applications, 69, 8, 2677-2682 (2008) · <a href="/1161.34001" class="nowrap">Zbl 1161.34001</a> · <a href="https://doi.org/10.1016/j.na.2007.08.042" class="nowrap">doi:10.1016/j.na.2007.08.042</a></td> </tr><tr> <td>[3]</td> <td class="space">Lakshmikantham, V.; Vatsala, A. 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V., Theory of Fractional Dynamic Systems (2009), Cambridge Scientific Publishers · <a href="/1188.37002" class="nowrap">Zbl 1188.37002</a></td> </tr><tr> <td>[6]</td> <td class="space">Lakshmikantham, V.; Leela, S., Differential and Integral Inequalities, Vol I and II (1969), New York, NY, USA: Academic Press, New York, NY, USA · <a href="/0177.12403" class="nowrap">Zbl 0177.12403</a></td> </tr><tr> <td>[7]</td> <td class="space">Li, Y.; Chen, Y.; Podlubny, I., Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability, Computers & Mathematics with Applications, 59, 5, 1810-1821 (2010) · <a href="/1189.34015" class="nowrap">Zbl 1189.34015</a> · <a href="https://doi.org/10.1016/j.camwa.2009.08.019" class="nowrap">doi:10.1016/j.camwa.2009.08.019</a></td> </tr><tr> <td>[8]</td> <td class="space">Choi, S. 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M., Sur l’intégrable de Laplace-Abel, Comptes Rendus de l’Académie des Sciences Series II, 136, 937-939 (1903) · <a href="/33.0408.01" class="nowrap">JFM 33.0408.01</a></td> </tr><tr> <td>[13]</td> <td class="space">Peng, J.; Li, K., A note on property of the Mittag-Leffler function, Journal of Mathematical Analysis and Applications, 370, 2, 635-638 (2010) · <a href="/1194.30002" class="nowrap">Zbl 1194.30002</a> · <a href="https://doi.org/10.1016/j.jmaa.2010.04.031" class="nowrap">doi:10.1016/j.jmaa.2010.04.031</a></td> </tr><tr> <td>[14]</td> <td class="space">Caputo, M., Linear models of dissipation whose Q is almost frequency independent-II, Geophysical Journal of the Royal Astronomical Society, 13, 529-539 (1967) · <a href="https://doi.org/10.1111/j.1365-246X.1967.tb02303.x" class="nowrap">doi:10.1111/j.1365-246X.1967.tb02303.x</a></td> </tr><tr> <td>[15]</td> <td class="space">Pinto, M., Perturbations of asymptotically stable differential systems, Analysis, 4, 1-2, 161-175 (1984) · <a href="/0568.34035" class="nowrap">Zbl 0568.34035</a></td> </tr><tr> <td>[16]</td> <td class="space">Li, Y.; Chen, Y.; Podlubny, I., Mittag-Leffler stability of fractional order nonlinear dynamic systems, Automatica, 45, 8, 1965-1969 (2009) · <a href="/1185.93062" class="nowrap">Zbl 1185.93062</a> · <a href="https://doi.org/10.1016/j.automatica.2009.04.003" class="nowrap">doi:10.1016/j.automatica.2009.04.003</a></td> </tr><tr> <td>[17]</td> <td class="space">Schneider, W. R., Completely monotone generalized Mittag-Leffler functions, Expositiones Mathematicae, 14, 1, 3-16 (1996) · <a href="/0843.60024" class="nowrap">Zbl 0843.60024</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>