Document Zbl 1312.34005

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Calc. Appl. Anal.</a> <a href="/?q=in%3A332283" title="Articles in this Issue">17, No. 2, 348-360 (2014)</a>. </div> <div class="abstract"><div class="pre">The authors are concerned with the existence and uniqueness of solutions for a coupled system of Hadamard type fractional differential equations and integral boundary conditions. The existence of solutions is derived from Leray-Schauder’s alternative, whereas the uniqueness of solution is established by Banach’s contraction principle. An illustrative example is also included.</div><div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A11097">Samir Bashir Hadid (Ajman)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6389406">Cited in <strong>106</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%3A34B10" title="MSC2020">34B10</a> </td> <td class="space"> Nonlocal and multipoint boundary value problems for ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47N20" title="MSC2020">47N20</a> </td> <td class="space"> Applications of operator theory to differential and integral equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afractional+derivatives+and+integrals">fractional derivatives and integrals</a>; <a href="/?q=ut%3AHadamard+fractional+derivative">Hadamard fractional derivative</a>; <a href="/?q=ut%3Ainitial+value+the+authors+problems">initial value the authors problems</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 1312.34005" data-ciurl="/ci/06389406" data-biburl="/bibtex/06389406.bib" data-amsurl="/amsrefs/06389406.bib" data-xmlurl="/xml/06389406.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06389406.pdf" title="Zbl 1312.34005 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/10.2478/s13540-014-0173-5" aria-label="DOI for “A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations”" title="10.2478/s13540-014-0173-5">DOI</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by-nc-nd/3.0/" 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"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/nc.svg" alt="Creative Commons NC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/nd.svg" alt="Creative Commons ND license icon" class="cc-license-icon"> </a> <img tabindex="0" src="/static/img/unlock_up.svg" class="cc-license-icon" title="Open version available"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">R.P. Agarwal, B. Ahmad, Existence theory for anti-periodic boundary value problems of fractional differential equations and inclusions. Comput. Math. Appl. 62 (2011), 1200-1214. http://dx.doi.org/10.1016/j.camwa.2011.03.001; · <a href="/1228.34009" class="nowrap">Zbl 1228.34009</a></td> </tr><tr> <td>[2]</td> <td class="space">A. Aghajani, Y. Jalilian, J.J. Trujillo, On the existence of solutions of fractional integro-differential equations. Fract. Calc. Appl. Anal. 15, No 1 (2012), 44-69; DOI: 10.2478/s13540-012-0005-4; http://link.springer.com/article/10.2478/s13540-012-0005-4.; · <a href="/1279.45008" class="nowrap">Zbl 1279.45008</a></td> </tr><tr> <td>[3]</td> <td class="space">B. Ahmad, J.J. Nieto, Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions. Comput. Math. Appl. 58 (2009), 1838-1843. http://dx.doi.org/10.1016/j.camwa.2009.07.091; · <a href="/1205.34003" class="nowrap">Zbl 1205.34003</a></td> </tr><tr> <td>[4]</td> <td class="space">B. Ahmad, J.J. Nieto, J. Pimentel, Some boundary value problems of fractional differential equations and inclusions. Comput. Math. Appl. 62 (2011), 1238-1250. http://dx.doi.org/10.1016/j.camwa.2011.02.035; · <a href="/1228.34011" class="nowrap">Zbl 1228.34011</a></td> </tr><tr> <td>[5]</td> <td class="space">B. Ahmad, J.J. Nieto, Anti-periodic fractional boundary value problems with nonlinear term depending on lower order derivative. Fract. Calc. Appl. Anal. 15, No 3 (2012), 451-462; DOI: 10.2478/s13540-012-0032-1; http://link.springer.com/article/10.2478/s13540-012-0032-1.; · <a href="/1281.34005" class="nowrap">Zbl 1281.34005</a></td> </tr><tr> <td>[6]</td> <td class="space">B. Ahmad, S.K. Ntouyas, Fractional differential inclusions with fractional separated boundary conditions, Fract. Calc. Appl. Anal. 15, No 3 (2012), 362-382; DOI: 10.2478/s13540-012-0027-y; http://link.springer.com/article/10.2478/s13540-012-0027-y.; · <a href="/1279.34003" class="nowrap">Zbl 1279.34003</a></td> </tr><tr> <td>[7]</td> <td class="space">B. Ahmad, S.K. Ntouyas, A. Alsaedi, New existence results for nonlinear fractional differential equations with three-point integral boundary conditions. Adv. Differ. Equ. 2011 (2011), Art. ID 107384, 11 pp.; · <a href="/1204.34005" class="nowrap">Zbl 1204.34005</a></td> </tr><tr> <td>[8]</td> <td class="space">B. Ahmad, S.K. Ntouyas, A four-point nonlocal integral boundary value problem for fractional differential equations of arbitrary order. Electron. J. Qual. Theory Differ. Equ. 2011, No 22 (2011), 15 pp.; · <a href="/1340.34063" class="nowrap">Zbl 1340.34063</a></td> </tr><tr> <td>[9]</td> <td class="space">D. Baleanu, R.P. Agarwal, O.G. Mustafa, M. Cosulschi, Asymptotic integration of some nonlinear differential equations with fractional time derivative. J. Phys. A, Math. Theor. 44, No 5 (2011), Article ID 055203, 9 p.; · <a href="/1238.26008" class="nowrap">Zbl 1238.26008</a></td> </tr><tr> <td>[10]</td> <td class="space">A. Cernea, A note on the existence of solutions for some boundary value problems of fractional differential inclusions. Fract. Calc. Appl. Anal. 15, No 2 (2012), 183-193; DOI: 10.2478/s13540-012-0013-4; http://link.springer.com/article/10.2478/s13540-012-0013-4.; · <a href="/1281.34019" class="nowrap">Zbl 1281.34019</a></td> </tr><tr> <td>[11]</td> <td class="space">N.J. Ford, M.L. Morgado, Fractional boundary value problems: analysis and numerical methods. Fract. Calc. Appl. Anal. 14, No 4 (2011), 554-567; DOI: 10.2478/s13540-011-0034-4; http://link.springer.com/article/10.2478/s13540-011-0034-4.; · <a href="/1273.65098" class="nowrap">Zbl 1273.65098</a></td> </tr><tr> <td>[12]</td> <td class="space">J.R. Graef, L. Kong, Q. Kong, W. Qingkai, M. 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Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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