I doubt the carriers will get the load of it. The US has bases in Italy and Germany that are in-range of Libya. Hell, we bombed Iraq from Alabama.
Relatively little of the air power will be US though. Most is going to be France, UK, and possibly UAE. UK will be operating out of Gibralter and France will be operating out of its own territory. Spain and Italy have also offered to host foreign air power at their bases.
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