Document Zbl 1247.34006

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Math. Appl.</a> <a href="/?q=in%3A299425" title="Articles in this Issue">63, No. 9, 1369-1381 (2012)</a>. </div> <div class="abstract">Summary: We discuss the existence and multiplicity of positive solutions for the singular fractional boundary value problem \[ D^{\alpha}_{0+}u(t)+f((t,u(t),D^{\nu}_{0+}u(t),D^{\mu}_{0+}u(t))=0, \]<br class="zbmathjax-paragraph">\[ u(0)=u'(0)=u''(0)=u''(1)=0, \] where $3<\alpha\leq 4$, $0<\nu\leq 1$, $1<\mu \leq 2$, $D^{\alpha}_{0+}$ is the standard Riemann-Liouville fractional derivative, $f$ is a Carathédory function and $f(t,x,y,z)$ is singular at the value $0$ of its arguments $x,y,z$. By means of a fixed point theorem, the existence and multiplicity of positive solutions are obtained.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6088468">Cited in <strong>109</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%3A34B18" title="MSC2020">34B18</a> </td> <td class="space"> Positive solutions to nonlinear boundary value problems for ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34B16" title="MSC2020">34B16</a> </td> <td class="space"> Singular nonlinear boundary value problems for ordinary differential equations </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+differential+equation">fractional differential equation</a>; <a href="/?q=ut%3Afixed+point+theorem">fixed point theorem</a>; <a href="/?q=ut%3ARiemann">Riemann</a>; <a href="/?q=ut%3ALiouville+fractional+derivative">Liouville fractional derivative</a>; <a href="/?q=ut%3Asingular+problem">singular problem</a>; <a href="/?q=ut%3Apositive+solution">positive solution</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 1247.34006" data-ciurl="/ci/06088468" data-biburl="/bibtex/06088468.bib" data-amsurl="/amsrefs/06088468.bib" data-xmlurl="/xml/06088468.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06088468.pdf" title="Zbl 1247.34006 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.camwa.2011.12.078" aria-label="DOI for “Existence and multiplicity of positive solutions for singular fractional boundary value problems”" title="10.1016/j.camwa.2011.12.078">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">Agarwal, R. 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