If you think about time travel you will quickly come to problems like the time paradox. In order to avoid a solution of the question about the paradox, the theory of multiple universes is used. Is there an approach that works without the multiple universes and yet does not contain a time paradox?
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Yes, there are several solutions.
Coming from Doctor Who it states that if you try to contact with another instance of yourself, some kind of energy will stop you from doing it. Another aspect is that you cannot change your past decisions.
In short, it states that despite you can travel back in time, you cannot change past. Instead, you being a time traveller are the cause of given present which sometimes might look like causal loop: you can be a father of yourself, for example. Whether to count it as a paradox, is on you, though. There is a novel where the main character becomes both a father and a mother of himself, which is an example of it applied. Can't remember the title, however. Another example is when Harry Potter travels the time.
This answer might not be comprehensive, people could come by with other solutions and if there are any, let others answer.