There is no shortage of time travel stories, or theories jow it could actually work. Often the differentiating point is how they handle paradoxes, the inevitable issues with moving through the time and offering the possibility to change the history/present/future. Maybe the most popular workaround is the multiverse explanation: every change in history creates a new timeline where nothing has seemingly changed while the old timeline continues with the original history. The more time travel the more parallel worlds get created.
In real quantum physics one of it's possible explanation is the so called many-worlds interpretation. Every possible world does exist for every action and choice made, down to the quantum level. So time travel could actually be just moving between these alternative worlds. But there wouldn't really be any point, you can't change anything as all those changes are already accounted for.
But back to the fiction. I like to think every time travel story being set in to the same multiverse. They just happen to be far enough apart from each other that the actual laws of time travel are different.
But if the multiverse theory is true and there is an infinite amount of universes with different rules would there be an universe where the theory of the multiverse isn't true?