jquery mobile drag and drop

This problem is known and has already been investigated.

It requires a correct .preventDefault() call in the right event handler.

Everything you need is here:

jQuery - draggable images on iPad / iPhone - how to integrate event.preventDefault();?

Hammer.js provides a powerful dragging feature. https://github.com/EightMedia/hammer.js

Excellent sample solutions:

jQuery UI Touch Punch is a small hack that enables the use of touch events on sites using the jQuery UI user interface library.

Currently, jQuery UI user interface library does not support the use of touch events in their widgets and interactions. This means that the slick UI you designed and tested in your desktop browser will fail on most, if not all, touch-enabled mobile devices, becuase jQuery UI listens to mouse events—mouseover, mousemove and mouseout—not touch events—touchstart, touchmove and touchend.

That's where jQuery UI Touch Punch comes in. Touch Punch works by using simulated events to map touch events to their mouse event analogs. Simply include the script on your page and your touch events will be turned into their corresponding mouse events to which jQuery UI will respond as expected.

As I said, Touch Punch is a hack. It duck punches some of jQuery UI's core functionality to handle the mapping of touch events...

http://ross.posterous.com/2008/08/19/iphone-touch-events-in-javascript/ contains an excellent code sniplet that converts touch events to mouse events:

function touchHandler(event)
{
    var touches = event.changedTouches,
        first = touches[0],
        type = "";

    switch(event.type)
    {
        case "touchstart": type = "mousedown"; break;
        case "touchmove":  type="mousemove"; break;        
        case "touchend":   type="mouseup"; break;
        default: return;
    }

    // initMouseEvent(type, canBubble, cancelable, view, clickCount,
    //                screenX, screenY, clientX, clientY, ctrlKey,
    //                altKey, shiftKey, metaKey, button, relatedTarget);

    var simulatedEvent = document.createEvent("MouseEvent");
    simulatedEvent.initMouseEvent(type, true, true, window, 1,
                              first.screenX, first.screenY,
                              first.clientX, first.clientY, false,
                              false, false, false, 0/*left*/, null);

    first.target.dispatchEvent(simulatedEvent);
    event.preventDefault();
}

function init()
{
    document.addEventListener("touchstart", touchHandler, true);
    document.addEventListener("touchmove", touchHandler, true);
    document.addEventListener("touchend", touchHandler, true);
    document.addEventListener("touchcancel", touchHandler, true);    
}