Document Zbl 1537.34007

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Capelas</a></div> <h2 class="title"> <strong>A system of Cauchy fractional differential equations and new properties of Mittag-Leffler functions with matrix argument.</strong> <i>(English)</i> <a class="label nowrap" href="/1537.34007">Zbl 1537.34007</a> </h2> <div class="source"> <a href="/serials/482" title="Journal Profile">J. Comput. Appl. Math.</a> <a href="/?q=in%3A476482" title="Articles in this Issue">406, Article ID 113977, 17 p. (2022)</a>. </div> <div class="abstract">Summary: Starting from the matrix form of the fractional Cauchy problem, new formulae for the sum of the three-parameter Mittag-Leffler functions are deduced. The derivation is based on the Prabhakar fractional integral operator. A Volterra integral equation relating the solution of the Cauchy problem with that of a perturbed problem is also obtained; from this a condition number measuring the sensitivity of the solution to changes in data can be derived. Several examples are also incorporated to test the bounds.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7472432">Cited in <strong>4</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%3A26A33" title="MSC2020">26A33</a> </td> <td class="space"> Fractional derivatives and integrals </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34A12" title="MSC2020">34A12</a> </td> <td class="space"> Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A44A10" title="MSC2020">44A10</a> </td> <td class="space"> Laplace transform </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34D10" title="MSC2020">34D10</a> </td> <td class="space"> Perturbations of ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A33E12" title="MSC2020">33E12</a> </td> <td class="space"> Mittag-Leffler functions and generalizations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A45J05" title="MSC2020">45J05</a> </td> <td class="space"> Integro-ordinary differential equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afractional+calculus">fractional calculus</a>; <a href="/?q=ut%3Ageneralized+Mittag-Leffler+functions">generalized Mittag-Leffler functions</a>; <a href="/?q=ut%3APrabhakar+derivative">Prabhakar derivative</a>; <a href="/?q=ut%3ALaplace+transform">Laplace transform</a>; <a href="/?q=ut%3Aconditioning">conditioning</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 1537.34007" data-ciurl="/ci/07472432" data-biburl="/bibtex/07472432.bib" data-amsurl="/amsrefs/07472432.bib" data-xmlurl="/xml/07472432.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07472432.pdf" title="Zbl 1537.34007 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.cam.2021.113977" aria-label="DOI for “A system of Cauchy fractional differential equations and new properties of Mittag-Leffler functions with matrix argument”" title="10.1016/j.cam.2021.113977">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">Abdalla, M., Special matrix functions: characteristics, achievements and future directions, Linear Multilinear Algebra, 68, 1-28 (2018) · <a href="/1427.15008" class="nowrap">Zbl 1427.15008</a></td> </tr><tr> <td>[2]</td> <td class="space">Garrappa, R.; Popolizio, M., Computing the matrix Mittag-Leffler function with applications to fractional calculus, J. 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