Steins Gate is probably the closest answer to this (in which the time travel mechanism can only send back information) and is my favorite time travel mechanics system. Timelines diverge into their infinite possibilities but in self consistent ways. That is, some timelines can only exist as a result of information received from other timeline’s future; meaning the past is dependent on the future of a different timeline which won’t play out, but has added a sort of immutable constant to the first timeline.