<script type="text/javascript" charset="utf-8">
    window.onload = function () {
        var container = jQuery('div.sliderGallery');
         var ul = jQuery('ul', container);

         var itemsWidth = ul.innerWidth() - container.outerWidth();

         jQuery('.slider', container).slider({
             min: 0,
             max: itemsWidth,
             handle: '.handle',
             stop: function (event, ui) {
                 ul.animate({'left' : ui.value * -1},340);
             },
             slide: function (event, ui) {
                 ul.css('left', ui.value * -1);
             }
         });
     };
</script>

// ...after all of Joomla's JS is done executing...

// before loading your version of jQuery var jquery = {}; // aka new Object()
jquery.joomla = jQuery.noConflict(); // moves jQuery into another namespace

// load your version

var J = jQuery.noConflict();

jQuery.noConflict();

<script type="text/javascript" charset="utf-8">
    $(document).ready(function () {
        var container = jQuery('div.sliderGallery');
         var ul = jQuery('ul', container);

         var itemsWidth = ul.innerWidth() - container.outerWidth();
         jQuery.noConflict();
         jQuery('.slider', container).slider({
             min: 0,
             max: itemsWidth,
             handle: '.handle',
             stop: function (event, ui) {
                 ul.animate({'left' : ui.value * -1},340);
             },
             slide: function (event, ui) {
                 ul.css('left', ui.value * -1);
             }
         });
     });
</script>