Document Zbl 1477.47057

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Funct. Spaces</a> <a href="/?q=in%3A373423" title="Articles in this Issue">2018, Article ID 7469868, 9 p. (2018)</a>. </div> <div class="abstract">Summary: We study the existence and uniqueness of positive solution for a class of nonlinear binary operator equations systems by means of the cone theory and monotone iterative technique, under more general conditions. Also, we give the iterative sequence of the solution and the error estimation of the system. Moreover, we use this new result to study the existence and uniqueness of the solutions for fractional differential equations systems involving integral boundary value conditions in ordered Banach spaces as an application. The results obtained in this paper are more general than many previous results and complement them.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6933357">Cited in <strong>24</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A47J05" title="MSC2020">47J05</a> </td> <td class="space"> Equations involving nonlinear operators (general) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47J26" title="MSC2020">47J26</a> </td> <td class="space"> Fixed-point iterations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34G20" title="MSC2020">34G20</a> </td> <td class="space"> Nonlinear differential equations in abstract spaces </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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aexistence">existence</a>; <a href="/?q=ut%3Auniqueness">uniqueness</a>; <a href="/?q=ut%3Apositive+solution">positive solution</a>; <a href="/?q=ut%3Anonlinear+binary+operator+equations">nonlinear binary operator equations</a>; <a href="/?q=ut%3Amonotone+iterative+technique">monotone iterative technique</a>; <a href="/?q=ut%3Afractional+differential+equations">fractional differential equations</a>; <a href="/?q=ut%3Aordered+Banach+spaces">ordered Banach spaces</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 1477.47057" data-ciurl="/ci/06933357" data-biburl="/bibtex/06933357.bib" data-amsurl="/amsrefs/06933357.bib" data-xmlurl="/xml/06933357.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06933357.pdf" title="Zbl 1477.47057 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/10.1155/2018/7469868" aria-label="DOI for “Fixed-point theorems for systems of operator equations and their applications to the fractional differential equations”" title="10.1155/2018/7469868">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">Chen, Y., Existence theorems of coupled fixed points, Journal of Mathematical Analysis and Applications, 154, 1, 142-150, (1991) · <a href="/0719.47041" class="nowrap">Zbl 0719.47041</a> · <a href="https://doi.org/10.1016/0022-247X(91)90076-C" class="nowrap">doi:10.1016/0022-247X(91)90076-C</a></td> </tr><tr> <td>[2]</td> <td class="space">Chen, Y., Fixed points of $T$-monotone operators, Nonlinear Analysis. 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