Mobile game engine are an alternative to native application programming. With native languages you need to program the engine your self, or make use of libraries. However there are lots of good alternatives out there to make mobile games.
I have made a list here of good alternatives programming tools, or mobile game engine to create mobile games. The list is presented in alphabetical order.
There are probably lots of other game engines. And most of these engines can publish to other platforms than mobile platforms too. Like web as Flash, html or a custom plugin. Some of the engines like Unreal Engine and Unity can publish to game consoles as well.
Engines like Stencyl and Construct 2 you dont even have to code your self. You just drag command blocks around. You kind of still have to code, but not from typing. It is worth to check out if you are a beginner into game design or game programming.
Check out the web pages for those engines.
So please download one of those engines and start making awesome games. Remember if you want to build native games you should check out Xcode, Android Studio or Visual Studio.
As you can see from the list, some of the mobile game engine are free, others are paid and some are subscription based. Some are free until your game reach over a certain amount of revenue. Then you have to pay a small percentage of royalty fee. Those limits are quite high, so you can easily afford it if it comes to that.