AFAICT the most mainstream view among physicists is the many worlds hypothesis - if time travel to the past is possible, the act of travelling to the past creates a branching timeline/universe. If you then go 'back to the future' you find yourself in a different timeline/universe than the one you left. But the traveller never gets 'deleted' or 'fades away'; they've simply shunted themselves out of their original timeline into the new timeline they created.
Not quite.
The Many Worlds Hypothesis* originally doesn't concern time travel. It first came up to resolve a troublesome bit of quantum mechanics - when a quantum waveform collapses - when we find out whether Schrodinger's Cat is alive or dead - why does it collapse one way, and not another? The Many-Worlds Hypothesis is that... it doesn't. It collapses in
all ways, but the life-experience that is you only sees one of them. In the ensemble of all universes, every choice that could have been made, every result that could have happened, does happen, and are seen by the different versions of you.
So, the act of time travel really doesn't need to create a branching universe - the branching universe
already exists.
Time travel came into it when someone realized that all the paradox issues of time travel are resolved if you cannot travel back to the exact timeline you came from, but you can only jump back into the past of one of the nearby branches - which is probably exactly like your own, because it only differs in how some John Q Public in Des Moines decided to get onion rings instead of fries with his burger that day.
*It is actually the Many Worlds Interpretation of quantum mechanics, as opposed to, say, the Copenhagen Interpretation. I am very loose with my language above, as it just makes it easier for people who don't want to get into the math.