Document Zbl 1544.93840

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Initially, the existence of a mild solution is established for the proposed Hilfer type fractional problem with novel ideas of non-instantaneous impulses. The non-linear alternative of Leray-Schauder type fixed point theorem, stochastic analysis, the measure of non-compactness and the multivalued analysis are applied to prove the mild solution. Further, the existence of optimal control is derived by employing Balder’s theorem. Finally, the application as a stochastic dam pollution model is provided to illustrate the developed theoretical results.<br class="zbmathjax-paragraph">© 2021 The Authors. IET Control Theory & Applications published by John Wiley & Sons, Ltd. on behalf of The Institution of Engineering and Technology</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7907160">Cited in <strong>12</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E20" title="MSC2020">93E20</a> </td> <td class="space"> Optimal stochastic control </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C27" title="MSC2020">93C27</a> </td> <td class="space"> Impulsive control/observation systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34K09" title="MSC2020">34K09</a> </td> <td class="space"> Functional-differential inclusions </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34K45" title="MSC2020">34K45</a> </td> <td class="space"> Functional-differential equations with impulses </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34K37" title="MSC2020">34K37</a> </td> <td class="space"> Functional-differential equations with fractional derivatives </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Astochastic+processes">stochastic processes</a>; <a href="/?q=ut%3Aoptimal+control">optimal control</a>; <a href="/?q=ut%3Adifferential+equations">differential equations</a>; <a href="/?q=ut%3ABalder+theorem">Balder theorem</a>; <a href="/?q=ut%3ASobolev-type+stochastic+Hilfer+fractional+noninstantaneous+impulsive+differential+inclusion">Sobolev-type stochastic Hilfer fractional noninstantaneous impulsive differential inclusion</a>; <a href="/?q=ut%3Astochastic+dam+pollution+model">stochastic dam pollution model</a>; <a href="/?q=ut%3Astochastic+analysis">stochastic analysis</a>; <a href="/?q=ut%3ALeray-Schauder+type+fixed+point+theorem">Leray-Schauder type fixed point theorem</a>; <a href="/?q=ut%3Anoninstantaneous+impulses">noninstantaneous impulses</a>; <a href="/?q=ut%3AClarke+subdifferential">Clarke subdifferential</a>; <a href="/?q=ut%3APoisson+jumps">Poisson jumps</a>; <a href="/?q=ut%3Aoptimal+control">optimal control</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 1544.93840" data-ciurl="/ci/07907160" data-biburl="/bibtex/07907160.bib" data-amsurl="/amsrefs/07907160.bib" data-xmlurl="/xml/07907160.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07907160.pdf" title="Zbl 1544.93840 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/10.1049/iet-cta.2019.0167" aria-label="DOI for “Optimal control of Sobolev-type stochastic Hilfer fractional non-instantaneous impulsive differential inclusion involving Poisson jumps and Clarke subdifferential”" title="10.1049/iet-cta.2019.0167">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, 1999, Academic Press: London · <a href="/0924.34008" class="nowrap">Zbl 0924.34008</a></td> </tr><tr> <td>[2]</td> <td class="space">Prathumwan, D.; 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