One of these frameworks is JQuery Mobile that is a great help in developing mobile app UIs across several platforms for mobile devices like Android and iOS. The advantage with this framework is code base that is extremely lightweight (weighing just 20KB when) in addition to several other elements like sliders and switches. If you do not like JQuery Mobile too much, you could try using some Moo Tools plugins that will help.
One other framework that is specifically meant to be used by developers who work on mobile devices that are HTML5 capable is Jo. In addition to Android and iOS, they can work on Chrome OS and webOS platforms as well. The framework has user interface elements like widgets for login screens in addition to the widget for popups that is helpful for providing additional information anytime a user needs it.
For development tasks like event handling and DOM manipulation, and good animation effects, developers can use the framework called xui.js which is meant for Internet Explorer or WebKit. Similarly EmbedJS is a framework meant for embedded devices like mobile phones, tablets and even TVs. It is armed with multiple builds and can be used on platforms and browsers like Firefox (Mozilla) Android and iOS. You also have access to the tool EmbedJS Build Tool that lets you customize your build. This framework is based on Dojo; hence developers used to the API Syntax (Dojo) can start using this framework without any hassles.