Document Zbl 1420.39005

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J. Math.</a> <a href="/?q=in%3A438862" title="Articles in this Issue">16, No. 5, Paper No. 113, 16 p. (2019)</a>. </div> <div class="abstract">Summary: This work is concerned with the existence and uniqueness of positive solutions to a nonlinear boundary value problem with fractional $q$-derivative: \[\begin{aligned} &D_q^\alpha u(t)+f(t,u(t),u(t))+g(t,u(t))=0, \quad 0<t<1 ,\\&u(0)=0 ,\quad u(1)=\beta u(\eta ), \end{aligned}\] where $D_q^\alpha$ is the fractional $q$-derivative of Riemann-Liouville type $, 0<q<1, 1<\alpha \le 2, 0<\eta <1,0<\beta \eta ^{\alpha -1}<1.$ By virtue of fixed-point theorems for mixed monotone operator, some existence and uniqueness results of positive solutions are obtained. An example to illustrate our results is given.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7110758">Cited in <strong>2</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A39A13" title="MSC2020">39A13</a> </td> <td class="space"> Difference equations, scaling ($q$-differences) </td> </tr><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%3A26A33" title="MSC2020">26A33</a> </td> <td class="space"> Fractional derivatives and integrals </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Apositive+solution">positive solution</a>; <a href="/?q=ut%3Amixed+monotone+operator">mixed monotone operator</a>; <a href="/?q=ut%3Afractional+%5C%28q%5C%29-difference+equation">fractional $q$-difference equation</a>; <a href="/?q=ut%3Aboundary+value+problem">boundary value problem</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 1420.39005" data-ciurl="/ci/07110758" data-biburl="/bibtex/07110758.bib" data-amsurl="/amsrefs/07110758.bib" data-xmlurl="/xml/07110758.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07110758.pdf" title="Zbl 1420.39005 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/s00009-019-1371-5" aria-label="DOI for “Positive solutions for a class of fractional boundary value problem with $q$-derivatives”" title="10.1007/s00009-019-1371-5">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">Oldham, K.B., Spanier, J.: The Fractional Calculus. 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