Document Zbl 1502.49028

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S.</a></div> <h2 class="title"> <strong>Using shifted Legendre orthonormal polynomials for solving fractional optimal control problems.</strong> <i>(English)</i> <a class="label nowrap" href="/1502.49028">Zbl 1502.49028</a> </h2> <div class="source"> <a href="/serials/8384" title="Journal Profile">Iran. J. Numer. Anal. Optim.</a> <a href="/?q=in%3A490331" title="Articles in this Issue">12, No. 3, 513-532 (2022)</a>. </div> <div class="abstract">Summary: Shifted Legendre orthonormal polynomials (SLOPs) are used to approximate the numerical solutions of fractional optimal control problems. To do so, first, the operational matrix of the Caputo fractional derivative, the SLOPs, and Lagrange multipliers are used to convert such problems into algebraic equations. Also, the method is proposed for solving multidimensional problems. We obtained the error bound of the operational matrix in fractional derivatives and proved the convergence of the method. Then, this is tested on some nonlinear examples. Comparison of our results with those obtained by other techniques in previous studies revealed the accuracy of the proposed technique for nonlinear and multidimensional problems.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7624661">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A49M25" title="MSC2020">49M25</a> </td> <td class="space"> Discrete approximations in optimal control </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A49J30" title="MSC2020">49J30</a> </td> <td class="space"> Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) </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><tr> <td> <a class="mono" href="/classification/?q=cc%3A42C05" title="MSC2020">42C05</a> </td> <td class="space"> Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afractional+optimal+control+problem+%28FOCP%29">fractional optimal control problem (FOCP)</a>; <a href="/?q=ut%3Ashifted+Legendre+orthonormal+polynomials+%28SLOPs%29">shifted Legendre orthonormal polynomials (SLOPs)</a>; <a href="/?q=ut%3ACaputo+fractional+derivative">Caputo fractional derivative</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 1502.49028" data-ciurl="/ci/07624661" data-biburl="/bibtex/07624661.bib" data-amsurl="/amsrefs/07624661.bib" data-xmlurl="/xml/07624661.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07624661.pdf" title="Zbl 1502.49028 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/10.22067/ijnao.2022.70466.1035" aria-label="DOI for “Using shifted Legendre orthonormal polynomials for solving fractional optimal control problems”" title="10.22067/ijnao.2022.70466.1035">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">Abdelhakem, M., Moussa, H., Baleanu, D.,and El-Kady, M. 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Bagherzadeh Using shifted Legendre or-thonormal polynomials for solving fractional optimal control problems. Ira-nian Journal of Numerical Analysis and Optimization, 2022; 12(3 (Special Issue), 2022): 513-532. doi: 10.22067/ijnao.2022.70466.1035. · <a href="/1502.49028" class="nowrap">Zbl 1502.49028</a> · <a href="https://doi.org/10.22067/ijnao.2022.70466.1035" class="nowrap">doi:10.22067/ijnao.2022.70466.1035</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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