Document Zbl 1484.34174

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Sousa, J. Vanterler</a>; <a href="/authors/de-oliveira.edmundo-capelas" title="Author Profile">de Oliveira, E. Capelas</a>; <a href="/authors/rodrigues.fabio-grangeiro" title="Author Profile">Rodrigues, F. G.</a></div> <h2 class="title"> <strong>Ulam-Hyers stabilities of fractional functional differential equations.</strong> <i>(English)</i> <a class="label nowrap" href="/1484.34174">Zbl 1484.34174</a> </h2> <div class="source"> <a href="/serials/8984" title="Journal Profile">AIMS Math.</a> <a href="/?q=in%3A481120" title="Articles in this Issue">5, No. 2, 1346-1358 (2020)</a>. </div> <div class="abstract">Summary: From the first results on Ulam-Hyers stability, what has been noted is the exponential growth of the researchers dedicated to investigating Ulam-Hyers stability of fractional differential equation solutions whether they are functional, evolution, impulsive, among others. However, some issues and problems still need to be addressed. An intensifying problem is the small amount of work on Ulam-Hyers stability of solutions of fractional functional differential equations through more general fractional operators. In this sense, in this paper, we present a study on the Ulam-Hyers and UlamHyers-Rassias stabilities of the solution of the fractional functional differential equation using the Banach fixed point theorem.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7515669">Cited in <strong>15</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A34K37" title="MSC2020">34K37</a> </td> <td class="space"> Functional-differential equations with fractional derivatives </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A26D15" title="MSC2020">26D15</a> </td> <td class="space"> Inequalities for sums, series and integrals </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3A%5C%28%5Cpsi%5C%29-Hilfer+fractional+derivative">$\psi$-Hilfer fractional derivative</a>; <a href="/?q=ut%3AUlam-Hyers+stability">Ulam-Hyers stability</a>; <a href="/?q=ut%3AUlam-Hyers-Rassias+stability">Ulam-Hyers-Rassias stability</a>; <a href="/?q=ut%3Afractional+functional+differential+equations">fractional functional differential equations</a>; <a href="/?q=ut%3ABanach+fixed+point+theorem">Banach fixed point theorem</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 1484.34174" data-ciurl="/ci/07515669" data-biburl="/bibtex/07515669.bib" data-amsurl="/amsrefs/07515669.bib" data-xmlurl="/xml/07515669.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07515669.pdf" title="Zbl 1484.34174 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/10.3934/math.2020092" aria-label="DOI for “Ulam-Hyers stabilities of fractional functional differential equations”" title="10.3934/math.2020092">DOI</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" 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">S. 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