Software Search - zbMATH Open

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software" 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>description</a></li> <li><a href="#"><span class="token item">au:</span><span>  </span>author</a></li> <li><a href="#"><span class="token item">cc:</span><span>  </span>msc</a></li> <li><a href="#"><span class="token item">pl:</span><span>  </span>programming language</a></li> <li><a href="#"><span class="token item">si:</span><span>  </span>software ID</a></li> <li><a href="#"><span class="token item">sw:</span><span>  </span>name</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="/software/?q=sw%3ASage%2A">sw:Sage*</a></span> <span class="search-explanation" role="cell" role="cell">Search for a specific <strong>s</strong>oft<strong>w</strong>are package containing the sequence <em>Sage</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/software/?q=ab%3Ageometry+%26+ut%3AORMS">ab:geometry & ut:ORMS</a></span> <span class="search-explanation" role="cell" role="cell">Search for software packages with the word <em>geometry</em> in the description(<strong>ab</strong>), and which have the keyword(<strong>ut</strong>) <em>ORMS</em> ( Oberwolfach Registry of Mathematical Software).The operator <strong>&</strong> is the default and may be omitted.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/software/?q=cc%3A13+%7C+14">cc:13 | 14</a></span> <span class="search-explanation" role="cell" role="cell">Search for software packages which are cited(<strong>cc</strong>) by articles belonging to the <strong><u>c</u>lassification <u>c</u>ode</strong> sections <em>13</em> and <em>14</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/software/?q=GAP+au%3AEick">GAP au:Eick</a></span> <span class="search-explanation" role="cell" role="cell">Search for <em>GAP</em> in the <strong>any</strong> index (which also includes dependencies) and by software <strong><u>au</u>thor</strong> containing the sequence <em>Eick</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/software/?q=pl%3AJava+%26+ab%3AR">pl:Java & ab:R</a></span> <span class="search-explanation" role="cell" role="cell">Search for software package in the <strong><u>p</u>rogramming <u>l</u>anguage</strong> Java whose description text(<strong>ab</strong>) contains <em>R</em></span> </div> </div> <h2>Fields</h2> <div id="help-fields" role="table"> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>ab</strong> </span> <span class="search-explanation" role="cell" role="cell"> Text from the description </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>au</strong> </span> <span class="search-explanation" role="cell" role="cell"> Name(s) of the author(s) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>cc</strong> </span> <span class="search-explanation" role="cell" role="cell"> Main fields of the software (given by first two MSC digits) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>pl</strong> </span> <span class="search-explanation" role="cell" role="cell"> Programming language the software is written in </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>si</strong> </span> <span class="search-explanation" role="cell" role="cell"> swMATH software ID </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>sw</strong> </span> <span class="search-explanation" role="cell" role="cell"> Software name </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>ut</strong> </span> <span class="search-explanation" role="cell" role="cell"> Keywords </span> </div> </div> <p style="margin-bottom:0.5cm;"></p> <h2>Operators</h2> <div id="operators-fields" role="table"> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>a & b</strong></span> <span class="search-explanation" role="cell" role="cell">logical and</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>a | b</strong></span> <span class="search-explanation" role="cell" role="cell">logical or</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>!ab</strong></span> <span class="search-explanation" role="cell" role="cell">logical not</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>abc*</strong></span> <span class="search-explanation" role="cell" role="cell">right wildcard</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>ab c</strong></span> <span class="search-explanation" role="cell" role="cell">phrase</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>(ab c)</strong></span> <span class="search-explanation" role="cell" role="cell">parentheses</span> </div> </div> <p style="margin-bottom:0.5cm;"></p> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> </div><div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="software"> <div class="content-main"> <article> <div class="head"> <h2>Mittag-Leffler</h2> </div> <div class="text"> <table> <tr> <td>swMATH ID:</td> <td> 12626 </td> </tr> <tr> <td>Software Authors:</td> <td> <div class="author"><a href="/authors/podlubny.igor" title="Author Profile">Podlubny, Igor</a></div> </td> </tr> <tr> <td>Description:</td> <td>Matlab File Exchange 8738. Mittag-Leffler function: This is a MATLAB routine for evaluating the Mittag-Leffler function with two parameters (sometimes also called generalized exponential function). The Mittag-Leffler function with two parameters plays an important role and appears frequently in solutions of fractional differential equations (i.e. differential equations containing fractional derivatives).</td> </tr> <tr> <td>Homepage:</td> <td> <a href="http://www.mathworks.com/matlabcentral/fileexchange/8738-mittag-leffler-function">http://www.mathworks.com/matlabcentral/fileexchange/8738-mittag-leffler-function</a> </td> </tr> <tr> <td>Dependencies:</td> <td>Matlab</td> </tr> <tr> <td>Related Software:</td> <td> <a href="/software/18400">mlf</a>; <a href="/software/558">Matlab</a>; <a href="/software/20907">ML</a>; <a href="/software/20918">ma2dfc</a>; <a href="/software/20908">mlrnd</a>; <a href="/software/8377">FODE</a>; <a href="/software/23743">mftoolbox</a>; <a href="/software/797">Regularization tools</a>; <a href="/software/24209">FracPECE</a>; <a href="/software/19507">FOTF Toolbox</a>; <a href="/software/20917">DFOC</a>; <a href="/software/20916">sysdfod</a>; <a href="/software/12185">Ninteger</a>; <a href="/software/4843">STABLE</a>; <a href="/software/11881">OPQ</a>; <a href="/software/554">Mathematica</a>; <a href="/software/22654">SubIval</a>; <a href="/software/7907">Robust Control Toolbox</a>; <a href="/software/4348">Simulink</a>; <a href="/software/14340">LSD</a> </td> </tr> <tr class="indexed"> <td>Cited in:</td> <td> <a href="/?q=si%3A12626">105 Documents</a> </td> </tr> </table> </div> <div class="profile"> <div class="facet1st"><a tabindex="0" class="more">all <i class="caret"></i></a> <a tabindex="0" class="less">top 5 <i class="caret"></i></a><h3>Cited by 175 Authors</h3> <table class="profile"> <tr> <td class="number"> <a href="/?q=si%3A12626+ai%3Amainardi.francesco" title="Citing Publications by this Author">8</a> </td> <td class="text"> <a href="/authors/mainardi.francesco" title="Author Profile"> Mainardi, Francesco </a> </td></tr><tr> <td class="number"> <a href="/?q=si%3A12626+ai%3Awei.ting" title="Citing Publications by 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this Field">55</a> </td> <td class="text"> <a href="/classification/?q=cc%3A65" title="Mathematics Subject Classification"> Numerical analysis <span style="white-space: nowrap;">(65-XX)</span> </a> </td></tr><tr> <td class="number"> <a href="/?q=si%3A12626+cc%3A26" title="Citing Publications in this Field">33</a> </td> <td class="text"> <a href="/classification/?q=cc%3A26" title="Mathematics Subject Classification"> Real functions <span style="white-space: nowrap;">(26-XX)</span> </a> </td></tr><tr> <td class="number"> <a href="/?q=si%3A12626+cc%3A33" title="Citing Publications in this Field">25</a> </td> <td class="text"> <a href="/classification/?q=cc%3A33" title="Mathematics Subject Classification"> Special functions <span style="white-space: nowrap;">(33-XX)</span> </a> </td></tr><tr> <td class="number"> <a href="/?q=si%3A12626+cc%3A34" title="Citing Publications in this Field">17</a> </td> <td class="text"> <a href="/classification/?q=cc%3A34" title="Mathematics Subject Classification"> Ordinary differential equations <span style="white-space: nowrap;">(34-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A45" title="Citing Publications in this Field">14</a> </td> <td class="text"> <a href="/classification/?q=cc%3A45" title="Mathematics Subject Classification"> Integral equations <span style="white-space: nowrap;">(45-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A60" title="Citing Publications in this Field">10</a> </td> <td class="text"> <a href="/classification/?q=cc%3A60" title="Mathematics Subject Classification"> Probability theory and stochastic processes <span style="white-space: nowrap;">(60-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A47" title="Citing Publications in this Field">8</a> </td> <td class="text"> <a href="/classification/?q=cc%3A47" title="Mathematics Subject Classification"> Operator theory <span style="white-space: nowrap;">(47-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A93" title="Citing Publications in this Field">6</a> </td> <td class="text"> <a href="/classification/?q=cc%3A93" title="Mathematics Subject Classification"> Systems theory; control <span style="white-space: nowrap;">(93-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A44" title="Citing Publications in this Field">5</a> </td> <td class="text"> <a href="/classification/?q=cc%3A44" title="Mathematics Subject Classification"> Integral transforms, operational calculus <span style="white-space: nowrap;">(44-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A82" title="Citing Publications in this Field">4</a> </td> <td class="text"> <a href="/classification/?q=cc%3A82" title="Mathematics Subject Classification"> Statistical mechanics, structure of matter <span style="white-space: nowrap;">(82-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A74" title="Citing Publications in this Field">3</a> </td> <td class="text"> <a href="/classification/?q=cc%3A74" title="Mathematics Subject Classification"> Mechanics of deformable solids <span style="white-space: nowrap;">(74-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A76" title="Citing Publications in this Field">3</a> </td> <td class="text"> <a href="/classification/?q=cc%3A76" title="Mathematics Subject Classification"> Fluid mechanics <span style="white-space: nowrap;">(76-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A92" title="Citing Publications in this Field">3</a> </td> <td class="text"> <a href="/classification/?q=cc%3A92" title="Mathematics Subject Classification"> Biology and other natural sciences <span style="white-space: nowrap;">(92-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A41" title="Citing Publications in this Field">2</a> </td> <td class="text"> <a href="/classification/?q=cc%3A41" title="Mathematics Subject Classification"> Approximations and expansions <span style="white-space: nowrap;">(41-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A62" title="Citing Publications in this Field">2</a> </td> <td class="text"> <a href="/classification/?q=cc%3A62" title="Mathematics Subject Classification"> Statistics <span style="white-space: nowrap;">(62-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A68" title="Citing Publications in this Field">2</a> </td> <td class="text"> <a href="/classification/?q=cc%3A68" title="Mathematics Subject Classification"> Computer science <span style="white-space: nowrap;">(68-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A42" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A42" title="Mathematics Subject Classification"> Harmonic analysis on Euclidean spaces <span style="white-space: nowrap;">(42-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A46" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A46" title="Mathematics Subject Classification"> Functional analysis <span style="white-space: nowrap;">(46-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A78" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A78" title="Mathematics Subject Classification"> Optics, electromagnetic theory <span style="white-space: nowrap;">(78-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A80" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A80" title="Mathematics Subject Classification"> Classical thermodynamics, heat transfer <span style="white-space: nowrap;">(80-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A86" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A86" title="Mathematics Subject Classification"> Geophysics <span style="white-space: nowrap;">(86-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A90" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A90" title="Mathematics Subject Classification"> Operations research, mathematical programming <span style="white-space: nowrap;">(90-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A91" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A91" title="Mathematics Subject Classification"> Game theory, economics, finance, and other social and behavioral sciences <span style="white-space: nowrap;">(91-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A12626+cc%3A94" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A94" title="Mathematics Subject Classification"> Information and communication theory, circuits <span style="white-space: nowrap;">(94-XX)</span> </a> </td></tr> </table> </div> <div class="diagram svg-diagram"> <h3>Citations by Year</h3> <div class="diagram si-diagram" aria-label="citing publications by year"></div> <style> rect:hover { fill: steelblue; } .axis path, .axis line { fill: none; stroke: #000; shape-rendering: crispEdges; } .bar { fill: steelblue; } a:hover .bar, a:focus .bar { stroke: black; fill-opacity: 60%; } </style> <script src="/static/js/d3.v3.min.js"></script> <script> var margin = { top: 20, right: 0, bottom: 30, left: 50 }; var width = 930 - margin.left - margin.right; var height = 150 - margin.top - margin.bottom; var svg = d3.selectAll(".si-diagram").append("svg") .attr("width", width + margin.left + margin.right) .attr("height", height + margin.top + margin.bottom) .append("g") .attr("transform", "translate(" + margin.left + "," + margin.top + ")"); var data = [{ year:2007, frequency:1 },{ year:2008, frequency:1 },{ year:2010, frequency:4 },{ year:2011, frequency:6 },{ year:2012, frequency:1 },{ year:2013, frequency:11 },{ year:2014, frequency:9 },{ year:2015, frequency:10 },{ year:2016, frequency:3 },{ year:2017, frequency:14 },{ year:2018, frequency:8 },{ year:2019, frequency:5 },{ year:2020, frequency:10 },{ year:2021, frequency:9 },{ year:2022, frequency:7 },{ year:2023, frequency:2 },{ year:2024, frequency:3 },{ year:2025, frequency:1 }]; data.forEach(function(d) { d.year = +d.year; d.frequency = +d.frequency; }); var xScale = d3.scale.ordinal() .rangeRoundBands([0, width], .1); var yScale = d3.scale.linear() .range([height, 0]); // fill if less than 20 years span var zero = d3.max( [ 20 - ( d3.max( data, d => d.year ) + 1 - d3.min( data, d => d.year ) ), 0 ] ); // generate range from min to max xScale.domain( d3.range( d3.min( data, d => d.year ), d3.max( data, d => d.year ) + 1 + zero ) ); yScale.domain( [ 0, d3.max( data, d => d.frequency ) ] ); var xAxis = d3.svg.axis() .scale(xScale) .tickValues( // show ticks every 5 years for range up to 50 years, every 10 // years up to 100 years, and every 20 years above that xScale.domain().filter( function(d, i) { let ticks; if (xScale.domain().length <= 50) { ticks = 5; } else if (xScale.domain().length <= 100) { ticks = 10; } else { ticks = 20; } return !(d % ticks); } ) ) .tickSize(6,3,0) // removes end tick .orient("bottom"); var yAxis = d3.svg.axis() .scale(yScale) .ticks(3) // number of ticks .tickFormat(d3.format("d")) // only integers .tickSize(6,3,0) // removes end tick .orient("left"); svg.selectAll(".bar") .data(data) .enter() .append("a") .attr( "xlink:href", d => "/?q=si%3A12626+py%3A" + d.year ) .attr( "title", d => d.frequency + " Publication" + (d.frequency > 1 ? "s" : "") + " in " + d.year ) .append("rect") .attr("class", "bar") .attr("x", d => xScale(d.year)) .attr("width", xScale.rangeBand()) .attr("y", d => yScale(d.frequency)) .attr("height", d => height - yScale(d.frequency)); svg.append("g") .attr("class", "x axis") .attr("transform", "translate(0," + height + ")") .call(xAxis); svg.append("g") .attr("class", "y axis") .call(yAxis) .append("text") .attr("transform", "rotate(-90)") .attr("y", 6) .attr("dy", ".75em") .style("text-anchor", "end") .text(""); </script> </div> </div> </article> </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>

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