We are aware of some problems that our controls have, when you use them on mobile browsers. We solved some of the problems for Q2 2010 SP1, however, the problem with the slider is not among them. We will do our best to improve the slider control in such scenarios for the official Q3 2010 release.
Regarding your question - you can move the dragHandle/thumb of the slider by changing its value. You can do this, using the client-side API of the control (set_value/set_selectionStart/set_selectionEnd methods in particular). Please refer to our online documentation for information on the API - http://www.telerik.com/help/aspnet-ajax/slider_clientobject.html
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