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Nonlinear Sci. Numer. Simul.</a> <a href="/?q=in%3A454290" title="Articles in this Issue">56, 314-329 (2018)</a>. </div> <div class="abstract">Summary: The Prabhakar function (namely, a three parameter Mittag-Leffler function) is investigated. This function plays a fundamental role in the description of the anomalous dielectric properties in disordered materials and heterogeneous systems manifesting simultaneous nonlocality and nonlinearity and, more generally, in models of Havriliak-Negami type. After reviewing some of the main properties of the function, the asymptotic expansion for large arguments is investigated in the whole complex plane and, with major emphasis, along the negative semi-axis. Fractional integral and derivative operators of Prabhakar type are hence considered and some nonlinear heat conduction equations with memory involving Prabhakar derivatives are studied.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7263244">Cited in <strong>85</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%3A26A33" title="MSC2020">26A33</a> </td> <td class="space"> Fractional derivatives and integrals </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35R11" title="MSC2020">35R11</a> </td> <td class="space"> Fractional partial differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A41A60" title="MSC2020">41A60</a> </td> <td class="space"> Asymptotic approximations, asymptotic expansions (steepest descent, etc.) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3APrabhakar+function">Prabhakar function</a>; <a href="/?q=ut%3AMittag-Leffler+function">Mittag-Leffler function</a>; <a href="/?q=ut%3Aasymptotic+expansion">asymptotic expansion</a>; <a href="/?q=ut%3Afractional+calculus">fractional calculus</a>; <a href="/?q=ut%3APrabhakar+derivative">Prabhakar derivative</a>; <a href="/?q=ut%3AHavriliak-Negami+model">Havriliak-Negami model</a>; <a href="/?q=ut%3Anonlinear+heat+equation">nonlinear heat equation</a></div> <div class="software"> <h3>Software:</h3><a href="/software/20907">ML</a></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 1524.33083" data-ciurl="/ci/07263244" data-biburl="/bibtex/07263244.bib" data-amsurl="/amsrefs/07263244.bib" data-xmlurl="/xml/07263244.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07263244.pdf" title="Zbl 1524.33083 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.2017.08.018" aria-label="DOI for “The Prabhakar or three parameter Mittag-Leffler function: theory and application”" title="10.1016/j.cnsns.2017.08.018">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1708.07298"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[2]</td> <td class="space">Al-Bassam, M. 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