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I have Nurgle Demon Prince with no wings , he's very fat.
Can cast warptime on himself ?

Let me put it this way-is there any reason he CAN'T?

Well it says someone within 3" , I wasn't sure if it had to be someone else within 3".

Read the core rules on aura abilities pg 5.

Well, since the CORE rules are literally free and available for download at GW:

Aura Abilities
Some units – usually Characters – have abilities that affect certain models within a given range. Unless the ability in question says otherwise, a model with a rule like this is always within range of the effect. For example, a Lord of Contagion has the Nurgle’s Gift ability, which affects all Death Guard models within 7" of him. As the Lord of Contagion is also a Death Guard model, he benefits from this ability as well.