白猫プロジェクト Shiro Neko Project is an action jrpg where you can collect characters and fight through stages. There's a story and unique one-handed controls.
AndroidNub: http://goo.gl/FWjYxb
Google play: https://play.google.com/store/apps/details?id=jp.colopl.wcat&hl=ja
Download: Download from QooApp
Requires internet connection.