Document Zbl 1334.65143

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Math. Comput.</a> <a href="/?q=in%3A355002" title="Articles in this Issue">242, 541-550 (2014)</a>. </div> <div class="abstract">Summary: Many physical processes appear to exhibit fractional order behavior that may vary with time and/or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider a new space-time variable fractional order advection-dispersion equation on a finite domain. The equation is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by Coimbra’s variable fractional derivative of order $\alpha(x) \in(0, 1]$, and the first-order and second-order space derivatives by the Riemann-Liouville derivatives of order $\gamma(x, t) \in(0, 1]$ and $\beta(x, t) \in(1, 2]$, respectively. We propose an implicit Euler approximation for the equation and investigate the stability and convergence of the approximation. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6574892">Cited in <strong>49</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M06" title="MSC2020">65M06</a> </td> <td class="space"> Finite difference methods for initial value and initial-boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M12" title="MSC2020">65M12</a> </td> <td class="space"> Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs </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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Avariable+fractional+derivative">variable fractional derivative</a>; <a href="/?q=ut%3Aadvection-dispersion+equation">advection-dispersion equation</a>; <a href="/?q=ut%3Aimplicit+Euler+scheme">implicit Euler scheme</a>; <a href="/?q=ut%3Astability">stability</a>; <a href="/?q=ut%3Aconvergence">convergence</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 1334.65143" data-ciurl="/ci/06574892" data-biburl="/bibtex/06574892.bib" data-amsurl="/amsrefs/06574892.bib" data-xmlurl="/xml/06574892.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06574892.pdf" title="Zbl 1334.65143 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.amc.2014.06.003" aria-label="DOI for “Numerical analysis of a new space-time variable fractional order advection-dispersion equation”" title="10.1016/j.amc.2014.06.003">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">Mehdinejadiani, Behrouz; Naseri, Abd Ali; Jafari, Hossein; Ghanbarzadeh, Afshin; Baleanu, Dumitru, A mathematical model for simulation of a water table profile between two parallel subsurface drains using fractional derivatives, Comput. 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