Touch-based devices like iPhone lacks all common mouse related events we are used to in desktop browsers. It does include: mousemove, mousedown, mouseup, among others.
So, the short answer is, you will need to use a solution that have in mind “touch events” counterparts for those “mouse events” above: touchstart, touchmove, touchend or touchcancel.
Take a look at this: https://github.com/furf/jquery-ui-touch-punch
You could be interested in jQuery mobile as well.
Hope it´s a start where you can find a proper solution for your requirements.