What is the best framework for creating mobile apps with HTML, CSS, and JavaScript?

Ionic framework is the best framework for creating mobile web apps.

phonegap or titanium for creating mobile apps with HTML

Ionic Framework is best for mobile apps for both android and ios.

for more reference goto http://ionicframework.com/docs/overview/

I recommend you to use Ionic2 + Angular2 to create hybrid mobile app.

Ionic2 is a framework built over Cordova. It offer among others UI Components which allow you to quickly construct an interface for your app with a render specific for the platform in which the app is built. 

Angular2 is a Javascript Framework which allow you to structure your application. It's recommended to use typescript language instead of javascript.

i have no idea about mobile app

jquery mobile is the best framework 

In the name of Allah the most merciful and beneficent.

Asalamualikum dear brothers and sisters,

Yes, I agree that JQuerryMobile is the best plate form for developing moblie apps simply by using html,css and savascripts but often though there are other plateform worth review for example;

Sencha Touch is a mobile framework powered by HTML5 and CSS3, providing APIs, animations, and components 

that are compatible with the current mobile platforms and browsers. Sencha Touch supports both Cordova and PhoneGap; 

you can compile your app, and submit your app to the respective platform’s App Stores. In addition, Sencha Touch provides a set of themes 

for iOS, Android, Blackberry, Windows Phone, Tizen, and a variety of other platforms to help your app feel like a native app.