Currently there is no application on the Google Play store, or the Apple App Store for NovelAI. However, NovelAI is available as a Progressive Web Application.
Installation on Android
To install a PWA, you need to open NovelAI's webpage in your mobile browser.
After that, open the browser's menu and look for an option like "Install" or "Add to home screen".
This will add a new icon to your home screen (it might be sent to a different page if it's full) to open up NovelAI. This removes all the browser headers and leaves more space for the interface.
Installation on IOS
The procedure is similar to installing NovelAI on Android, the option is just found in the "add to" section: Add to Home Screen.