Apply JQuery mobile style on button after add the button programmatically by javascript code

When I try to add below jquery mobile button throw jquery code:

        // insert new button to bf div (breackfast div)
      $("#bf").html('<a href="FoodCat/FilterIndex?TimeId=2&CurDate=0" data-role="button" > Add new </a> ');

It doesn't imply the Jquery mobile style (data-role="button") ??

Below is the html:

  <div data-role="collapsible-set" data-theme="i" data-split-icon="gear" data-split-theme="e">
      <div data-role="collapsible">

        <h3> Breackfast   </h3>
                 <div id="bf"  style="margin:0 !important;padding:0 !important; display:inline !important"> 
             <ul data-role="listview" data-theme="i" ">
              <li>

                <input type="button" tabindex="@ViewBag.CurInt" id="bdelete" value="DeleteFood" onclick="bfd();"/>
                 </li>
                  </ul>
                </div>
             </div>
          </div>

Below is the JQuery code (PLZ note: it call the service and do the delete, but the problem only in not render button as jquery mobile style)

               <script type="text/javascript">
                    function bfd() {
                       var fp = '/api/service?prsnIduser1&MealTime=2&CurDate='+ $("#bdelete").attr("tabindex");
                      $.ajax({
                            url: fp,
                            type: 'Delete',
                            dataType: 'json',
                            contentType: 'application/json;  charset=utf-8',
                        success: function () {

                          $("#bf").html('<a href="FoodCat/FilterIndex?TimeId=2&CurDate=0" data-role="button" > Add new </a> ');
                      $("#bf a").buttonMarkup();

                             });
                            }
                   </script>

I did many search on google and on stackoverflow, And unsuccessfully I attempt below but without resault :

        $("div[data-role=collapsible]").collapsible({refresh: true });
         // or even add :
           $("#bf").page();
          // or
           $("#bf a").buttonMarkup();

If I understood you correctly, you want to dynamically create a jQuery Mobile button and have it styled correctly.

Here's a working jsFiddle example: http://jsfiddle.net/Gajotres/m4rjZ/

$(document).on('pagebeforeshow', '#index', function(){    
    // Add a new button element
    $('[data-role="content"]').append('<a id="button" href="FoodCat/FilterIndex?TimeId=2&CurDate=0" data-role="button">Button</a>');
    // Enhance new button element
    $('#button').button();
});

To find out more about how jQuery Mobile handles dynamically added content and how it can be enhanced take a look at this ARTICLE, or find it HERE.

Here's a link to an official jQuery Mobile button documentation.