Clock is built-in app on iPhone or iPad can set the timer for automatic turn off Youtube and make your iPhone and iPad to sleep mode. Just tab the clock app and go to Timer > When Timer Ends > Stop Playing then choose the time you want to set and tab Start button.
You should use this feature when you fell asleep and keep Youtube video on. That will make iPone or iPad battery is dead. No more wake up at night to turn off iPhone playing Youtube video anymore. This feature can use timer with Music app or, live tv apps or when you play video page on Safari.