Document Zbl 1442.65140

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This system is transformed to a type of weakly singular integral equations in which the weak singular kernel is involved with both the unknown and known functions. The regularity and existence of its solution is studied. The collocation methods on discontinuous piecewise polynomial space are considered. The convergence and superconvergence properties of the introduced methods are derived on graded meshes. Numerical results provided to show that our theoretical convergence bounds are often sharp and the introduced methods are efficient. Some comparisons and applications are discussed.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7252589">Cited in <strong>71</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65L60" title="MSC2020">65L60</a> </td> <td class="space"> Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65L03" title="MSC2020">65L03</a> </td> <td class="space"> Numerical methods for functional-differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M06" title="MSC2020">65M06</a> </td> <td class="space"> Finite difference methods for initial value and initial-boundary value problems involving PDEs </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%3Asystem+of+fractional+differential+equations">system of fractional differential equations</a>; <a href="/?q=ut%3Adiscontinuous+piecewise+polynomial+spaces">discontinuous piecewise polynomial spaces</a>; <a href="/?q=ut%3Aoperational+matrices">operational matrices</a>; <a href="/?q=ut%3AMittag-Leffler+function">Mittag-Leffler function</a>; <a href="/?q=ut%3Acollocation+methods">collocation methods</a>; <a href="/?q=ut%3Adiffusion+equations">diffusion 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 1442.65140" data-ciurl="/ci/07252589" data-biburl="/bibtex/07252589.bib" data-amsurl="/amsrefs/07252589.bib" data-xmlurl="/xml/07252589.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07252589.pdf" title="Zbl 1442.65140 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.chaos.2018.09.020" aria-label="DOI for “Collocation methods for fractional differential equations involving non-singular kernel”" title="10.1016/j.chaos.2018.09.020">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">Podlubny, I., Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, 198 (1998), Academic press · <a href="/0922.45001" class="nowrap">Zbl 0922.45001</a></td> </tr><tr> <td>[2]</td> <td class="space">Caputo, M., Linear models of dissipation whose q is almost frequency independentii, Geophys J Int, 13, 5, 529-539 (1967)</td> </tr><tr> <td>[3]</td> <td class="space">Caputo, M.; Fabrizio, M., A new definition of fractional derivative without singular kernel, Prog Fractional Differ Appl, 1, 2, 1-13 (2015)</td> </tr><tr> <td>[4]</td> <td class="space">Losada, J.; Nieto, J. 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