Which framework is the best to develop a mobile application using database connection?
There's no "best" framework. Depends on the context of your question. It's very vague, give more information.
First of all you have to know on what Operating System do you want to go.
Then you have to create some restfull api's that comunicate with your database.
You can use HTML5 included in your android or ios, or create your interface with the api's.
My humble opinion would be to opt for a framework like CodeIgnitor and Twitter Bootstrap.
But then we don't know EXACTLY what you want to do?
How about Yii? Haven't tried it as I am focused on CakePHP but my buddy said that it(Yii) would automatically set-up the CSS which depends on your screen resolution(this has to be confirmed).
Kevinyu, Bootstrap is the needed framework for the screen resolution, at least one of them.
To be honest I had many concerns about jQuery , and I still have. But I use it. So sure http://jquerymobile.com/demos/1.2.1/ is a clean logic for the UI . But the UI is just the end point , the model , the data structure and how controller does it is the main. And UI isn’t the view.