Document Zbl 1504.34226

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Document Zbl 1504.34226 - zbMATH Open</title> <meta name="viewport" content="width=device-width, minimum-scale=0.1, maximum-scale=5.0"> <meta name="robots" content="noarchive, noindex"> <meta name="referrer" content="origin-when-cross-origin"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap-theme.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.css" rel="stylesheet" media="screen,print"> <link rel="stylesheet" href="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/css/bootstrap-select.min.css"> <link href="/static/css/smoothness/jquery-ui-1.10.1.custom.min.css" rel="stylesheet" media="screen"> <link href="/static/styles.css?v=20241024" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/zbMathJax/v0.1.38/zbmathjax.css" rel="stylesheet" media="screen,print"> <link rel="shortcut icon" href="/static/zbmath.ico"> <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "Organization", "url": "https://zbmath.org/", "logo": "https://zbmath.org/static/zbMATH.png" } </script> </head> <body> <div id="line"></div> <span id="clear" style="cursor: pointer;">×</span> <div id="page"> <div id="head"> <nav id="menu" class="navbar navbar-default"> <div class="container-fluid"> <div class="navbar-header"> <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#zbnav" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button> <a class="navbar-brand" href="#"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open logo"> </a> </div> <div id="zbnav" class="collapse navbar-collapse"> <ul class="nav navbar-nav pages"> <li class="about"> <a href="/about/">About</a> </li> <li class="frequently-asked-questions"> <a href="/frequently-asked-questions/">FAQ</a> </li> <li class="general-help"> <a href="/general-help/">General Help</a> </li> <li class="reviewer-service"> <a href="https://zbmath.org/reviewer-service/" target="_self" >Reviewer Service</a> </li> <li> <a href="/tools-and-resources/">Tools & Resources</a> </li> <li class="contact"> <a href="/contact/">Contact</a> </li> </ul> <ul class="nav navbar-nav navbar-right prefs"> <li class="preferences dropdown"> <a data-toggle="dropdown" href="#">Preferences <i class="caret"></i></a> <ul class="dropdown-menu preferences"> <li> <form id="preferences" class="navbar-form" method="post" action="/preferences/" onsubmit="return confirm('This website uses cookies for the purposes of storing preference information on your device. Do you agree to this?\n\nPlease refer to our Privacy Policy to learn more about our use of cookies.')" > <input type="hidden" name="path" value="/?q=rf%3A6600049+ai%3Ayahia.ibrahim-s"> <span class=""> <label class="title">Search Form</label> <div class="form-group"> <input id="search-multi-line" type="radio" name="search" value="multi-line" checked> <label for="search-multi-line" class="radio">Multi-Line Search (default)</label> </div> <div class="form-group"> <input id="search-one-line" type="radio" name="search" value="one-line"> <label for="search-one-line" class="radio">One-Line Search</label> </div> </span> <span class="count"> <label class="title">Hits per Page</label> <div class="form-group"> <input id="count-10" type="radio" name="count" value="10"> <label for="count-10" class="radio">10</label> </div> <div class="form-group"> <input id="count-20" type="radio" name="count" value="20"> <label for="count-20" class="radio">20</label> </div> <div class="form-group"> <input id="count-50" type="radio" name="count" value="50"> <label for="count-50" class="radio">50</label> </div> <div class="form-group"> <input id="count-100" type="radio" name="count" value="100" checked> <label for="count-100" class="radio">100 (default)</label> </div> <div class="form-group"> <input id="count-200" type="radio" name="count" value="200"> <label for="count-200" class="radio">200</label> </div> </span> <span class="format"> <label class="title">Display Format</label> <div class="form-group"> <input id="format-mathjax" type="radio" name="format" value="mathjax" checked> <label for="format-mathjax" class="radio">MathJax (default)</label> </div> <div class="form-group"> <input id="format-amstex" type="radio" name="format" value="latex"> <label for="format-amstex" class="radio">LaTeX</label> </div> </span> <span class="ranking"> <label class="title">Documents Sorting</label> <div class="form-group"> <input id="documents-ranking-default" type="radio" name="documents_ranking" value="date" checked> <label for="documents-ranking-default" class="radio">Newest first (default)</label> </div> <div class="form-group"> <input id="documents-ranking-references" type="radio" name="documents_ranking" value="references"> <label for="documents-ranking-references" class="radio">Citations</label> </div> <div class="form-group"> <input id="documents-ranking-relevance" type="radio" name="documents_ranking" value="relevance"> <label for="documents-ranking-relevance" class="radio">Relevance</label> </div> </span> <span class="ranking"> <label class="title">Authors Sorting</label> <div class="form-group"> <input id="authors-ranking-default" type="radio" name="authors_ranking" value="alpha" checked> <label for="authors-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="authors-ranking-references" type="radio" name="authors_ranking" value="references"> <label for="authors-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Serials Sorting</label> <div class="form-group"> <input id="serials-ranking-default" type="radio" name="serials_ranking" value="alpha" checked> <label for="serials-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="serials-ranking-references" type="radio" name="serials_ranking" value="references"> <label for="serials-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Software Sorting</label> <div class="form-group"> <input id="software-ranking-default" type="radio" name="software_ranking" value="references" checked> <label for="software-ranking-default" class="radio">Citations (default)</label> </div> <div class="form-group"> <input id="software-ranking-alpha" type="radio" name="software_ranking" value="alpha"> <label for="software-ranking-alpha" class="radio">Alphabetically</label> </div> </span> <button type="submit" class="btn btn-default">OK</button> <div class="clearfix"> </form> </li> </ul> </li> </ul> </div> </div> </nav> <div id="tabs"> <h1 class="logo"> <a class="logo" href="/"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open — the first resource for mathematics" > </a> </h1> <nav> <ul class="nav nav-tabs"> <li class="tab-documents active"> <a href="/">Documents</a> </li> <li class="tab-authors"> <a href="/authors/">Authors</a> </li> <li class="tab-serials"> <a href="/serials/">Serials</a> </li> <li class="tab-software"> <a href="/software/">Software</a> </li> <li class="tab-classification"> <a href="/classification/">Classification</a> </li> <li class="tab-formulae"> <a href="/formulae/">Formulæ</a> </li> </ul> </nav> <div class="clearfix"></div> </div> <div class="content-fixed"> <div class="content-formular"> <div style="display: none;"> <div class="row ml-0"id="multi-line-new-line" style="display: none;"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-0-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-0-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input"> <span class="multi-line-value" id="multi-line-type-range"><span style="padding-left: 5px;">from</span> <input name="ml-0-v1" class="form-control multi-line-input" type="text" value="" aria-label="value"> until <input name="ml-0-v2" class="form-control multi-line-input" type="text" value="" aria-label="value"></span> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-la" placeholder="use name or ISO code"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-rv" placeholder="enter name or zbMATH reviewer number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-an" placeholder="Zbl, JFM or ERAM number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-en" placeholder="e.g. DOI, ISBN, arXiv ID"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-sw" placeholder="use * to find all documents using software"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-br" placeholder="find documents about the life or work of a person"> <span class="multi-line-value" id="multi-line-type-multiselect-db"> <select class="multi-line-selectpicker" data-width="100%" multiple> <option value="zbl">Zbl</option> <option value="arxiv">arXiv</option> <option value="jfm">JFM</option> <option value="eram">ERAM</option> </select> <input type="hidden" class="multi-line-input" name="ml-0-v" value=""> </span> </div> <form name="documents" method="GET" action="/" autocomplete="off"> <div class="documents multi-line" style="display: none;"> <div class="forms"> <ul class="nav forms"> <li class="one-line"> <span tabindex="0" class="glyphicon glyphicon-question-sign" title="One-Line Search allows for free logical combinations of search fields" aria-label="One-Line Search allows for free logical combinations of search fields" data-placement="bottom"></span> <a style="display: inline-block;" href="#">One-Line Search <span class="glyphicon glyphicon-search"></span></a> </li> </ul> </div> <div class="clearfix"></div> <div class="container-fluid"> <input type="hidden" id="multi-line-ml" name="ml" value="3"> <div id="multi-line-row-wrapper"> <div class="row ml-1"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-1-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-1-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-1-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-2"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-2-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au" selected>Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-2-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-2-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-3"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-3-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti" selected>Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-3-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><div id="multi-line-plus"> <a href="#"><span class="glyphicon glyphicon-plus" aria-hidden="true"></span> add line</a> </div></div> </div> </div> <div class="row"> <div class="col-xs-12 form-inline"> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-test" style="visibility: hidden; position: fixed;"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label title="search for Articles in Journals"> <input type="checkbox" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label title="search for arXiv Preprints"> <input type="checkbox" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-real"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label for="dt-j" title="search for Articles in Journals"> <input type="checkbox" id="dt-j" name="dt" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label for="dt-a" title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" id="dt-a" name="dt" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label for="dt-b" title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" id="dt-b" name="dt" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label for="dt-p" title="search for arXiv Preprints"> <input type="checkbox" id="dt-p" name="dt" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> </div> </div> <div class="row"> <div class="col-xs-12 buttons"> <a tabindex="0" class="btn btn-default clear-all">Reset all <span class="glyphicon glyphicon-remove"></span></a> <div class="submit"> <button class="btn btn-default search" type="submit">Search <span class="glyphicon glyphicon-search"></span></button> </div> </div> </div> </div> </div> </form> <form class="form-inline" name="documents" method="GET" action="/"> <div class="documents one-line" style="display: block;"> <div class="forms"> <ul class="nav forms"> <li class="multi-line"><a href="#">New Multi-Line Search <span class="glyphicon glyphicon-list"></span></a></li> </ul> </div> <div id="search-row" class="input-group box"> <span> <div id="search-field"> <input class="query form-control" type="text" name="q" value="rf:6600049 ai:yahia.ibrahim-s" aria-label="Search for documents" placeholder="Search for documents" autocomplete="off"> </div> <div class="search-buttons input-group-btn"> <div class="btn-group"> <button class="btn btn-default search" type="submit"><span class="virtual">Search</span> <span class="glyphicon glyphicon-search" style="top: 2px;"></span></button> </div> </div> </span> <span> <div class="search-buttons input-group-btn"> <div class="btn-group"> <div class="btn-group fields"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Fields <i class="caret"></i></button> <ul id="fields" class="dropdown-menu pull-right"> <li><a href="#"><span class="token item">any:</span><span> </span>anywhere (default)</a></li> <li><a href="#"><span class="token item">ab:</span><span>  </span>review text</a></li> <li><a href="#"><span class="token item">an:</span><span>  </span>zbmath id</a></li> <li><a href="#"><span class="token item">any:</span><span>  </span>anywhere</a></li> <li><a href="#"><span class="token item">au:</span><span>  </span>contributor name</a></li> <li><a href="#"><span class="token item">br:</span><span>  </span>biographic reference name</a></li> <li><a href="#"><span class="token item">cc:</span><span>  </span>msc title</a></li> <li><a href="#"><span class="token item">dt:</span><span>  </span>document type</a></li> <li><a href="#"><span class="token item">doi:</span><span>  </span>doi</a></li> <li><a href="#"><span class="token item">en:</span><span>  </span>external id</a></li> <li><a href="#"><span class="token item">la:</span><span>  </span>language</a></li> <li><a href="#"><span class="token item">pu:</span><span>  </span>publisher</a></li> <li><a href="#"><span class="token item">py:</span><span>  </span>year</a></li> <li><a href="#"><span class="token item">rv:</span><span>  </span>reviewer name</a></li> <li><a href="#"><span class="token item">so:</span><span>  </span>source</a></li> <li><a href="#"><span class="token item">sw:</span><span>  </span>software name</a></li> <li><a href="#"><span class="token item">ti:</span><span>  </span>title</a></li> <li><a href="#"><span class="token item">ut:</span><span>  </span>keyword</a></li> </ul> </div> <div class="btn-group operators"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Operators <i class="caret"></i></button> <ul id="operators" class="dropdown-menu pull-right"> <li><a href="#"><span class="token">a <span class="item">&</span> b </span><span> </span>logical and (default)</a></li> <li><a href="#"><span class="token">a <span class="item">|</span> b </span><span> </span>logical or</a></li> <li><a href="#"><span class="token"><span class="item">!</span>ab   </span><span> </span>logical not</a></li> <li><a href="#"><span class="token">abc<span class="item">*</span>  </span><span> </span>right wildcard</a></li> <li><a href="#"><span class="token"><span class="item">"</span>ab c<span class="item">"</span></span><span> </span>phrase</a></li> <li><a href="#"><span class="token"><span class="item">(</span>ab c<span class="item">)</span></span><span> </span>parentheses</a></li> </ul> </div> </div> </div> <div class="special"> <ul class="nav help-button"> <li class="dropdown pull-right"> <a href="#">Help <i class="caret"></i></a> </li> </ul> </div> </span> </div> <div class="help"><h2>Examples</h2> <div id="help-terms" role="table"> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Geometry">Geometry</a></span> <span class="search-explanation" role="cell" role="cell">Search for the term <em>Geometry</em> in <strong>any</strong> field. Queries are <strong>case-independent</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Funct%2A">Funct*</a></span> <span class="search-explanation" role="cell"><strong>Wildcard</strong> queries are specified by <strong><u>*</u></strong> (e.g. <em>functions</em>, <em>functorial</em>, etc.). Otherwise the search is <strong>exact</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Topological+group%22">"Topological group"</a></span> <span class="search-explanation" role="cell"><strong>Phrases</strong> (multi-words) should be set in <u>"</u>straight quotation marks<u>"</u>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=au%3A+Bourbaki+%26+ti%3A+Algebra">au: Bourbaki & ti: Algebra</a></span> <span class="search-explanation" role="cell">Search for <strong><u>au</u>thor</strong> and <strong><u>ti</u>tle</strong>. The <strong>and-operator &</strong> is default and can be omitted.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Chebyshev+%7C+Tschebyscheff">Chebyshev | Tschebyscheff</a></span> <span class="search-explanation" role="cell">The <strong>or-operator |</strong> allows to search for <em>Chebyshev</em> or <em>Tschebyscheff</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Quasi%2A+map%2A+py%3A+1989">Quasi* map* py: 1989</a></span> <span class="search-explanation" role="cell">The resulting documents have <strong><u>p</u>ublication <u>y</u>ear</strong> <em>1989</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=so%3A+Eur%2A+J%2A+Mat%2A+Soc%2A+cc%3A+14">so: Eur* J* Mat* Soc* cc: 14</a></span> <span class="search-explanation" role="cell">Search for publications in a particular <strong><u>so</u>urce</strong> with a <strong>Mathematics Subject <u>C</u>lassification <u>c</u>ode (<u>cc</u>)</strong> in <em>14</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Partial+diff%2A+eq%2A%22+%21+elliptic">"Partial diff* eq*" ! elliptic</a></span> <span class="search-explanation" role="cell">The <strong>not</strong>-operator <strong>!</strong> eliminates all results containing the word <em>elliptic</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=dt%3A+b+%26+au%3A+Hilbert">dt: b & au: Hilbert</a></span> <span class="search-explanation" role="cell">The <strong><u>d</u>ocument <u>t</u>ype</strong> is set to books; alternatively: <u>j</u> for <strong>journal articles</strong>, <u>a</u> for <strong>book articles</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=py%3A+2000-2015+cc%3A+%2894A+%7C+11T%29">py: 2000-2015 cc: (94A | 11T)</a></span> <span class="search-explanation" role="cell">Number <strong>ranges</strong> are accepted. Terms can be grouped within <strong><u>(</u>parentheses<u>)</u></strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=la%3A+chinese">la: chinese</a></span> <span class="search-explanation" role="cell">Find documents in a given <strong><u>la</u>nguage</strong>. <a href="http://en.wikipedia.org/wiki/ISO_639-1">ISO 639-1</a> language codes can also be used.</span> </div> </div> <div id="help-fields"> <h2>Fields</h2> <table> <tr> <td class="nowrap padding" role="rowheader"><strong>any</strong></td> <td class="padding">anywhere</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>an</strong></td> <td class="padding">internal document identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>au</strong></td> <td class="padding">author, editor</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ai</strong></td> <td class="padding">internal author identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ti</strong></td> <td class="padding">title</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>la</strong></td> <td class="padding">language</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>so</strong></td> <td class="padding">source</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ab</strong></td> <td class="padding">review, abstract</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>py</strong></td> <td class="padding">publication year</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>rv</strong></td> <td class="padding">reviewer</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>cc</strong></td> <td class="padding">MSC code</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ut</strong></td> <td class="padding">uncontrolled term</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>dt</strong></td> <td class="padding" colspan="4">document type (<strong>j</strong>: journal article; <strong>b</strong>: book; <strong>a</strong>: book article)</td> </tr> </table> </div> <div id="help-operators"> <h2>Operators</h2> <table> <tr> <td class="nowrap padding" role="rowheader">a <strong>&</strong> b</td> <td class="padding">logic and</td> </tr> <tr> <td class="nowrap padding" role="rowheader">a <strong>|</strong> b</td> <td class="padding">logic or</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>!</strong>ab</td> <td class="padding">logic not</td> </tr> <tr> <td class="nowrap padding" role="rowheader">abc<strong>*</strong></td> <td class="padding">right wildcard</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>"</strong>ab c<strong>"</strong></td> <td class="padding">phrase</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>(</strong>ab c<strong>)</strong></td> <td class="padding">parentheses</td> </tr> </table> </div> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> <div class="clearfix"></div> </div> <div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="documents"> <div class="content-main"> <div class="content-item"><div class="item"> <article> <div class="author"><a href="/authors/sooppy-nisar.kottakkaran" title="Author Profile">Sooppy Nisar, Kottakkaran</a>; <a href="/authors/ravichandran.chokkalingam" title="Author Profile">Ravichandran, C.</a>; <a href="/authors/abdel-aty.abdel-haleem" title="Author Profile">Abdel-Aty, Abdel-Haleem</a>; <a href="/authors/yahia.ibrahim-s" title="Author Profile">Yahia, Ibrahim S.</a>; <a href="/authors/park.choonkil" title="Author Profile">Park, Choonkil</a></div> <h2 class="title"> <strong>Case study on total controllability and optimal control of Hilfer neutral non-instantaneous fractional derivative.</strong> <i>(English)</i> <a class="label nowrap" href="/1504.34226">Zbl 1504.34226</a> </h2> <div class="source"> <a href="/serials/2026" title="Journal Profile">Fractals</a> <a href="/?q=in%3A486149" title="Articles in this Issue">30, No. 5, Article ID 2240187, 17 p. (2022)</a>. </div> <div class="abstract">Summary: The aim of the study is to discuss the controllability results of Hilfer neutral non-instantaneous impulsive fractional integro-differential equations (HNNIIFIE). Total controllability results were discussed by employing set-contraction theory and Kuratowski measure of non-compactness. Also we derived the results on optimal control using appropriate conditions. An illustration is given to validate the outcomes.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7578043">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%3A34K30" title="MSC2020">34K30</a> </td> <td class="space"> Functional-differential equations in abstract spaces </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34K34" title="MSC2020">34K34</a> </td> <td class="space"> Hybrid systems of functional-differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34K40" title="MSC2020">34K40</a> </td> <td class="space"> Neutral functional-differential equations </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%3A34K35" title="MSC2020">34K35</a> </td> <td class="space"> Control problems for functional-differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B05" title="MSC2020">93B05</a> </td> <td class="space"> Controllability </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><tr> <td> <a class="mono" href="/classification/?q=cc%3A49J27" title="MSC2020">49J27</a> </td> <td class="space"> Existence theories for problems in abstract spaces </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AHilfer+derivative">Hilfer derivative</a>; <a href="/?q=ut%3Atotal+controllability">total controllability</a>; <a href="/?q=ut%3AKuratowski+measure">Kuratowski measure</a>; <a href="/?q=ut%3Anon-instantaneous+impulses">non-instantaneous impulses</a>; <a href="/?q=ut%3ABanach+space">Banach space</a>; <a href="/?q=ut%3Afractional+calculus">fractional calculus</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 1504.34226" data-ciurl="/ci/07578043" data-biburl="/bibtex/07578043.bib" data-amsurl="/amsrefs/07578043.bib" data-xmlurl="/xml/07578043.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07578043.pdf" title="Zbl 1504.34226 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/10.1142/S0218348X22401879" aria-label="DOI for “Case study on total controllability and optimal control of Hilfer neutral non-instantaneous fractional derivative”" title="10.1142/S0218348X22401879">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">Kucche, K. D., Kharade, J. P. and Sousa, J. V. C., On the nonlinear impulsive $\operatorname{\Psi} $-Hilfer fractional differential equations, Math. Model. Anal. (2020), https://doi.org/10.3846/mma.2020.11445. · <a href="/1491.34013" class="nowrap">Zbl 1491.34013</a></td> </tr><tr> <td>[2]</td> <td class="space">Chen, P., Zhang, X. and Li, Y., Existence of mild solutions to partial differential equations with non-instantaneous impulses, Electron. J. Differ. Equ.241 (2016) 1-11. · <a href="/1350.34047" class="nowrap">Zbl 1350.34047</a></td> </tr><tr> <td>[3]</td> <td class="space">Kumar, V., Malik, M. and Debbouche, A., Total controllability of neutral fractional differential equation with non-instantaneous impulsive effects, J. Comput. Appl. Math.383 (2021) 113158. · <a href="/1448.93029" class="nowrap">Zbl 1448.93029</a></td> </tr><tr> <td>[4]</td> <td class="space">Saravanakumar, S. and Balasubramaniam, P., Non-instantaneous impulsive Hilfer fractional stochastic differential equations driven by fractional Brownian motion, Stoch. Anal. Appl.39(3) (2021) 549-566. · <a href="/1475.60109" class="nowrap">Zbl 1475.60109</a></td> </tr><tr> <td>[5]</td> <td class="space">Yang, H. and Zhao, Y., Existence and optimal controls of non-autonomous impulsive integro-differential evolution equation with nonlocal conditions, Chaos Solitons Fractals148 (2021) 111027. · <a href="/1485.49014" class="nowrap">Zbl 1485.49014</a></td> </tr><tr> <td>[6]</td> <td class="space">Wang, J. R., Ibrahim, G., O’Regan, D. and Zhou, Y., A general class of non-instantaneous fractional differential inclusions in Banach spaces, Adv. Difference Equ.287(2017) (2017), https://doi.org/10.1186/s13662-017-1342-8.</td> </tr><tr> <td>[7]</td> <td class="space">Wang, J. R., Ibrahim, G. and O’Regan, D., Controllability of Hilfer fractional non-instantaneous impulsive semilinear differential inclusions with nonlocal conditions, Nonlinear Anal. Model. Control24(6) (2019) 958-984. · <a href="/1439.34015" class="nowrap">Zbl 1439.34015</a></td> </tr><tr> <td>[8]</td> <td class="space">Wang, J. R. and Zhang, Y., Nonlocal initial value problems for differential equations with Hilfer fractional derivative, Appl. Math. Comput.266 (2015) 850-859. · <a href="/1410.34032" class="nowrap">Zbl 1410.34032</a></td> </tr><tr> <td>[9]</td> <td class="space">Hernández, E. and O’Regan, D., On a new class of abstract impulsive differential equations, Proc. Amer. Math. Soc.141(5) (2013) 1641-1649. · <a href="/1266.34101" class="nowrap">Zbl 1266.34101</a></td> </tr><tr> <td>[10]</td> <td class="space">Pierri, M., O’Regan, D. and Rolnik, V., Existence of solutions for semi-linear abstract differential equations with not instantaneous impulses, Appl. Math. Comput.219(12) (2013) 6743-6749. · <a href="/1293.34019" class="nowrap">Zbl 1293.34019</a></td> </tr><tr> <td>[11]</td> <td class="space">Fečkan, M., Wang, J. and Zhou, Y., Existence of periodic solutions for nonlinear evolution equations with non-instantaneous impulses, Nonauton. Dyn. Syst.1 (2014) 93-101. · <a href="/1311.34094" class="nowrap">Zbl 1311.34094</a></td> </tr><tr> <td>[12]</td> <td class="space">Hilfer, R., Applications of Fractional Calculus in Physics (World Scientific, Singapore, 2000). · <a href="/0998.26002" class="nowrap">Zbl 0998.26002</a></td> </tr><tr> <td>[13]</td> <td class="space">Furati, K. M., Kassim, M. D. and Tatar, N. E., Existence and uniqueness for a problem involving Hilfer fractional derivative, Comput. Math. Appl.64(6) (2012) 1616-1626. · <a href="/1268.34013" class="nowrap">Zbl 1268.34013</a></td> </tr><tr> <td>[14]</td> <td class="space">Gu, H. and Trujillo, J. J., Existence of mild solution for evolution equation with Hilfer fractional derivative, Appl. Math. Comput.257 (2015) 344-354. · <a href="/1338.34014" class="nowrap">Zbl 1338.34014</a></td> </tr><tr> <td>[15]</td> <td class="space">Hilfer, R., Luchko, Y. and Tomovski, Z., Operational method for the solution of fractional differential equations with generalized Riemann-Liouville fractional derivatives, Fract. Calc. Appl. Anal.12(3) (2009) 289-318. · <a href="/1182.26011" class="nowrap">Zbl 1182.26011</a></td> </tr><tr> <td>[16]</td> <td class="space">Subashini, R., Jothimani, K., Nisar, K. S. and Ravichandran, C., New results on nonlocal functional integro-differential equations via Hilfer fractional derivative, Alex. Eng. J.59(5) (2020) 2891-2899.</td> </tr><tr> <td>[17]</td> <td class="space">J. V. C. Sousa, Existence of mild solutions to Hilfer fractional evolution equations in Banach space, Class. Anal. ODEs, doi:1812.02213v1. · <a href="/1458.34032" class="nowrap">Zbl 1458.34032</a></td> </tr><tr> <td>[18]</td> <td class="space">Agarwal, P., Baleanu, D., Quan, Y., Momani, C. S. and Machado, J. A., Fractional Calculus-Models, Algorithms, Technology (Springer, Singapore, 2018).</td> </tr><tr> <td>[19]</td> <td class="space">Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J., Theory and Applications of Fractional Differential Equations, , Vol. 204 (Elsevier Science, Amsterdam, 2006). · <a href="/1092.45003" class="nowrap">Zbl 1092.45003</a></td> </tr><tr> <td>[20]</td> <td class="space">Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations (Springer-Verlag, New York, 1983). · <a href="/0516.47023" class="nowrap">Zbl 0516.47023</a></td> </tr><tr> <td>[21]</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 (Academic Press, San Diego, 1999). · <a href="/0924.34008" class="nowrap">Zbl 0924.34008</a></td> </tr><tr> <td>[22]</td> <td class="space">Zhou, Y., Basic Theory of Fractional Differential Equations (World Scientific, Singapore, 2014). · <a href="/1336.34001" class="nowrap">Zbl 1336.34001</a></td> </tr><tr> <td>[23]</td> <td class="space">Debbouche, A. and Baleanu, D., Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems, Comput. Math. Appl.62(3) (2011) 1442-1450. · <a href="/1228.45013" class="nowrap">Zbl 1228.45013</a></td> </tr><tr> <td>[24]</td> <td class="space">Kavitha, K., Vijayakumar, V. and Udhayakumar, R., Results on controllability of Hilfer fractional neutral differential equations with infinite delay via measures of noncompactness, Chaos Solitons Fractals139 (2020) 1-9. · <a href="/1490.34091" class="nowrap">Zbl 1490.34091</a></td> </tr><tr> <td>[25]</td> <td class="space">Nisar, K. S., Jothimani, K., Kaliraj, K. and Ravichandran, C., An analysis of controllability results for nonlinear Hilfer neutral fractional derivatives with non-dense domain, Chaos Solitons Fractals146 (2021) 110915. · <a href="/1498.34215" class="nowrap">Zbl 1498.34215</a></td> </tr><tr> <td>[26]</td> <td class="space">Kailasavalli, S., Baleanu, D., Suganya, S. and Arjunan, M. M., Exact controllability of fractional neutral integro-differential systems with state-dependent delay in Banach spaces, An. Cst. Univ. Ovidius Constanta24(1) (2016) 29-55. · <a href="/1389.93041" class="nowrap">Zbl 1389.93041</a></td> </tr><tr> <td>[27]</td> <td class="space">Wang, X., Wang, L. and Zeng, Q., Fractional differential equations with integral boundary conditions, J. Nonlinear Sci. Appl.8(4) (2015) 309-314. · <a href="/1312.34028" class="nowrap">Zbl 1312.34028</a></td> </tr><tr> <td>[28]</td> <td class="space">Kavitha, K., Vijayakumar, V., Udhayakumar, R. and Ravichandran, C., Results on controllability of Hilfer fractional differential equations with infinite delay via measures of noncompactness, Asian J. Control (2021), https://doi.org/10.1002/asjc.2549. · <a href="/1490.34091" class="nowrap">Zbl 1490.34091</a></td> </tr><tr> <td>[29]</td> <td class="space">Jajarmi, A., Pariz, N., Effati, S. and Kamyad, A. V., Infinite horizon optimal control for nonlinear interconnected large-scale dynamical systems with an application to optimal attitude control, Asian J. Control14(5) (2011) 1239-1250. · <a href="/1303.93021" class="nowrap">Zbl 1303.93021</a></td> </tr><tr> <td>[30]</td> <td class="space">Baleanu, D., Sajjadi, S. S., Jajarmi, A. and Defterli, Ö., On a nonlinear dynamical system with both chaotic and nonchaotic behaviors: A new fractional analysis and control, Adv. Differ. Equ.2021 (2021), https://doi.org/10.1186/s13662-021-03393-x. · <a href="/1494.34138" class="nowrap">Zbl 1494.34138</a></td> </tr><tr> <td>[31]</td> <td class="space">Baleanu, D., Sajjadi, S. S., Asad, J. H., Jajarmi, A. and Estiri, E., Hyperchaotic behaviors, optimal control, and synchronization of a nonautonomous cardiac conduction system, Adv. Differ. Equ.2021 (2021), https://doi.org/10.1186/s13662-021-03320-0. · <a href="/1494.34137" class="nowrap">Zbl 1494.34137</a></td> </tr><tr> <td>[32]</td> <td class="space">Baleanu, D., Zibaei, S., Namjoo, M. and Jajarmi, A., A nonstandard finite difference scheme for the modeling and nonidentical synchronization of a novel fractional chaotic system, Adv. Differ. Equ.2021 (2021), https://doi.org/10.1186/s13662-021-03454-1. · <a href="/1494.65060" class="nowrap">Zbl 1494.65060</a></td> </tr><tr> <td>[33]</td> <td class="space">Jajarmi, A., Baleanu, D., Vahid, K. Z. and Mobayen, S., A general fractional formulation and tracking control for immunogenic tumor dynamics, Math. Methods Appl. Sci.45(2) (2021) 667-680. · <a href="/1531.92026" class="nowrap">Zbl 1531.92026</a></td> </tr><tr> <td>[34]</td> <td class="space">Valliammal, N. and Ravichandran, C., Results on fractional neutral integro-differential systems with state dependent delay in Banach spaces, Nonlinear Stud.25(1) (2018) 159-171. · <a href="/1476.34155" class="nowrap">Zbl 1476.34155</a></td> </tr><tr> <td>[35]</td> <td class="space">Jothimani, K., Valliammal, N. and Ravichandran, C., Existence result for a neutral fractional integrodifferential equation with state dependent delay, J. Appl. Nonlinear Dyn.7(4) (2018) 371-381. · <a href="/1407.34012" class="nowrap">Zbl 1407.34012</a></td> </tr><tr> <td>[36]</td> <td class="space">Nisar, K. S., Logeswari, K., Vijayaraj, V., Baskonus, H. M. and Ravichandran, C., Fractional order modeling the gemini virus in capsicum annuum with optimal control, Fractal Fract.61 (2022), https://doi.org/10.3390/fractalfract6020061.</td> </tr><tr> <td>[37]</td> <td class="space">Goufo, E. F. Doungmo, Ravichandran, C. and Birajdar, G. A., Self-similarity techniques for chaotic attractors with many scrolls using step series switching, Math. Model. Anal.26(4) (2021) 591-611. · <a href="/1497.28004" class="nowrap">Zbl 1497.28004</a></td> </tr><tr> <td>[38]</td> <td class="space">Bahaa, G. M., Optimal control problem and maximum principle for fractional order cooperative systems, Kybernetika55(2) (2019) 337-358. · <a href="/1463.49005" class="nowrap">Zbl 1463.49005</a></td> </tr><tr> <td>[39]</td> <td class="space">Gupta, V., Jarad, F., Valliammal, N., Ravichandran, C. and Nisar, K. S., Existence and uniqueness of solutions for fractional nonlinear hybrid impulsive system, Numer. Methods Part. Differ. Equ.38(3) (2022) 359-371. · <a href="/1536.34006" class="nowrap">Zbl 1536.34006</a></td> </tr><tr> <td>[40]</td> <td class="space">Kaliraj, K., Thilakraj, E., Ravichandran, C. and Nisar, K. S., Controllability analysis for impulsive integro-differential equation via Atangana-Baleanu fractional derivative, Math. Methods Appl. Sci. (2021) 1-10, https://doi.org/10.1002/mma.7693.</td> </tr><tr> <td>[41]</td> <td class="space">Harrat, A., Nieto, J. J. and Debbouche, A., Solvability and optimal controls of impulsive Hilfer fractional delay evolution inclusions with Clarke subdifferential, J. Comput. Appl. Math.344 (2018) 725-737. · <a href="/1393.49026" class="nowrap">Zbl 1393.49026</a></td> </tr><tr> <td>[42]</td> <td class="space">Pan, X., Li, X. and Zhao, J., Solvability and optimal controls of semi linear Riemann-Liouville fractional differential equations, Abstr. Appl. Anal.2014 (2014) 216919. · <a href="/1472.49013" class="nowrap">Zbl 1472.49013</a></td> </tr><tr> <td>[43]</td> <td class="space">Zhu, S., Fan, Z. and Li, G., Optimal controls for Riemann-Liouville fractional evolution systems without Lipschitz assumption, J. Optim. Theory Appl.174 (2017) 47-64. · <a href="/1378.49004" class="nowrap">Zbl 1378.49004</a></td> </tr><tr> <td>[44]</td> <td class="space">Chitalkar-Dhaigude, C., Bhairat, S. P. and Dhaigude, D., Solution of fractional differential equations involving Hilfer fractional derivative: Method of successive approximations, Bull. Marathwada Math. Soc.18(2) (2017) 1-13.</td> </tr><tr> <td>[45]</td> <td class="space">Rezazadeh, H., Aminikhah, H. and Sheikhani, A. Refahi, Stability analysis of Hilfer fractional differential systems, Math. Commun.21(1) (2016) 45-64. · <a href="/1345.26015" class="nowrap">Zbl 1345.26015</a></td> </tr><tr> <td>[46]</td> <td class="space">Banaś, J., On measures of noncompactness in Banach spaces, Comment. Math. Univ. Carolin.21(1) (1980) 131-143. · <a href="/0438.47051" class="nowrap">Zbl 0438.47051</a></td> </tr><tr> <td>[47]</td> <td class="space">Balder, E., Necessary and sufficient conditions for l 1-strong-weak lower semi-continuity of integral functional, Nonlinear Anal.11(1) (1987) 399-404.</td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. 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. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

CINXE.COM

Document Zbl 1504.34226 - zbMATH Open