Document Zbl 1380.93038

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M.</a></div> <h2 class="title"> <strong>Mathematical modeling of fractional differential filtration dynamics based on models with Hilfer-Prabhakar derivative.</strong> <i>(English. Russian original)</i> <a class="label nowrap" href="/1380.93038">Zbl 1380.93038</a> </h2> <div class="source"> <a href="/serials/1809" title="Journal Profile">Cybern. Syst. Anal.</a> <a href="/?q=in%3A366443" title="Articles in this Issue">53, No. 2, 204-216 (2017)</a>; translation from Kibern. Sist. Anal. 2017, No. 2, 51-64 (2017). </div> <div class="abstract">Summary: We construct a generalized mathematical model to describe the fractional differential dynamics of filtration processes in fractured porous media, based on the use of the concept of Hilfer-Prabhakar fractional derivative. Within the framework of this model, we obtain a number of closed form solutions to boundary-value problems of filtration theory for modeling the dynamics of pressures at launch of wells in case of plane-radial filtration, as well as by activity of galleries under plane-parallel filtration.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6837664">Cited in <strong>20</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td class="mono"> 93A30 </td> <td class="space"> Mathematical modelling of systems (MSC2010) </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%3A76S05" title="MSC2020">76S05</a> </td> <td class="space"> Flows in porous media; filtration; seepage </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Amathematical+modeling">mathematical modeling</a>; <a href="/?q=ut%3Afractional+differential+dynamics+of+filtration+processes">fractional differential dynamics of filtration processes</a>; <a href="/?q=ut%3Afractured+porous+media">fractured porous media</a>; <a href="/?q=ut%3Anon-classical+models">non-classical models</a>; <a href="/?q=ut%3Aequation+of+filtration+with+Hilfer-Prabhakar+fractional+derivative">equation of filtration with Hilfer-Prabhakar fractional derivative</a>; <a href="/?q=ut%3Aboundary-value+problems">boundary-value problems</a>; <a href="/?q=ut%3Aclosed+form+solutions">closed form solutions</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 1380.93038" data-ciurl="/ci/06837664" data-biburl="/bibtex/06837664.bib" data-amsurl="/amsrefs/06837664.bib" data-xmlurl="/xml/06837664.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06837664.pdf" title="Zbl 1380.93038 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/10.1007/s10559-017-9920-z" aria-label="DOI for “Mathematical modeling of fractional differential filtration dynamics based on models with Hilfer-Prabhakar derivative”" title="10.1007/s10559-017-9920-z">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">S. 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Bulavatskiy, “Some mathematical models of geoinformatics for describing mass transfer processes under time-nonlocal conditions,” J. Autom. Inform. Sci., Vol. 43, Issue 6, 49-59 (2011). · <a href="https://doi.org/10.1615/JAutomatInfScien.v43.i6.50" class="nowrap">doi:10.1615/JAutomatInfScien.v43.i6.50</a></td> </tr><tr> <td>[10]</td> <td class="space">V. M. Bulavatsky, “Nonclassical mathematical model in geoinformatics to solve dynamic problems for nonequilibrium nonisothermal seepage fields,” Cybern. and Syst. Analysis, Vol. 47, No. 6, 898-906 (2011). · <a href="/1302.86019" class="nowrap">Zbl 1302.86019</a> · <a href="https://doi.org/10.1007/s10559-011-9369-4" class="nowrap">doi:10.1007/s10559-011-9369-4</a></td> </tr><tr> <td>[11]</td> <td class="space">V. M. Bulavatsky and Yu. G. Krivonos, “Mathematical modelling in the geoinformation problem of the dynamics of geomigration under space-time nonlocality,” Cybern. and Syst. 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Dubbeldam, “Generalized Langevin equation with a tree parameter Mittag-Leffler noise,” Physica A, Vol. 390, No. 21, 3627-3636 (2011). · <a href="https://doi.org/10.1016/j.physa.2011.05.039" class="nowrap">doi:10.1016/j.physa.2011.05.039</a></td> </tr><tr> <td>[24]</td> <td class="space">H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Oxford Science Publications, Oxford University Press (1986). · <a href="/0584.73001" class="nowrap">Zbl 0584.73001</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. 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