jQuery Mobile offers support for a wide range of platforms; they categorize browsers according to A-, B-, and C-level groupings, as below. A-level browsers can exploit full functionality (though, as the docs note, the "visual fidelity of the experience and smoothness of page transitions are highly dependent on the CSS rendering capabilities of the device and platform so not all A grade experience will be pixel-perfect but that's the nature of the web." See the jQuery Mobile docs for the current full list of supported devices.
|A-grade||Full enhanced experience with Ajax-based animated page transitions|
|B-grade||Enhanced experience except without Ajax navigation features|
|C-grade||Basic, non-enhanced HTML experience that is still functional|