Document Zbl 1441.35213

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(2020)</a>. </div> <div class="abstract">Summary: In this paper, the fractional order models are used to study the propagation of ion-acoustic waves in ultrarelativistic plasmas in nonplanar geometry (cylindrical). Firstly, according to the control equations, $(2 + 1)$-dimensional (2D) cylindrical Kadomtsev-Petviashvili (CKP) equation and 2D cylindrical-modified Kadomtsev-Petviashvili (CMKP) equation are derived by using multiscale analysis and reduced perturbation methods. Secondly, using the semi-inverse method and the fractional variation principle, the abovementioned equations are derived the time-space fractional equations (TSF-CKP and TSF-CMKP). Furthermore, based on the fractional order transformation, the 1-decay mode solution of the TSF-CKP equation is obtained by using the simplified homogeneous balance method, and using the generalized hyperbolic-function method, the exact analytic solution of TSF-CMKP equation is obtained. Finally, the effects of the phase speed $\lambda $, electron number density (through $\beta_3)$ and the fractional order $\left( \alpha , \beta , \omega\right)$ on the propagation of ion-acoustic waves in ultrarelativistic plasmas are analyzed.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7199203">Cited in <strong>9</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q53" title="MSC2020">35Q53</a> </td> <td class="space"> KdV equations (Korteweg-de Vries equations) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q35" title="MSC2020">35Q35</a> </td> <td class="space"> PDEs in connection with fluid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76Y05" title="MSC2020">76Y05</a> </td> <td class="space"> Quantum hydrodynamics and relativistic hydrodynamics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76Q05" title="MSC2020">76Q05</a> </td> <td class="space"> Hydro- and aero-acoustics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A82D10" title="MSC2020">82D10</a> </td> <td class="space"> Statistical mechanics of plasmas </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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aion-acoustic+waves">ion-acoustic waves</a>; <a href="/?q=ut%3Aultrarelativistic+plasmas">ultrarelativistic plasmas</a>; <a href="/?q=ut%3AKadomtsev-Petviashvili+%28CKP%29+equations">Kadomtsev-Petviashvili (CKP) equations</a>; <a href="/?q=ut%3Atime-space+fractional+equations">time-space fractional equations</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 1441.35213" data-ciurl="/ci/07199203" data-biburl="/bibtex/07199203.bib" data-amsurl="/amsrefs/07199203.bib" data-xmlurl="/xml/07199203.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07199203.pdf" title="Zbl 1441.35213 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/10.1155/2020/9075823" aria-label="DOI for “Time-space fractional model for complex cylindrical ion-acoustic waves in ultrarelativistic plasmas”" title="10.1155/2020/9075823">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">Mamun, A. 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