If you wanted to operate unmodified Air Force planes from a carrier-type vehicle, then the ship would have to be enormous. Typically, tactical Air Force planes require a field several thousand feet long to take off and land. I've seen figures that show these planes need 3,000 to 5,000 feet of runway to take off and land safely. This could be reduced substancially if the ship is capable of high speed, say 30 knots. Still, you'd need somewhere around 2,000 foot long runways to operate planes like the F-15E without a catapault and arrestor gear.

Ok, then what about retrofitting those planes with the necessary equipment? Well, for one thing, the planes weren't built to handle the stresses of carrier operations. Navy planes are built with extra-strong fuselages and landing gear to withstand the stresses. In doing so, they deliberately sacriface useful load or some other characteristic to make up for the extra structural weight. Many Air Force planes have what looks like a tail hook but that's simply a device designed for limited use in case the plane is about to run off of a runway.

If you wanted to build such a gigantic floating ship capable of hosting Air Force planes, I'd suggest making it somewhere on the order of 1,500 to 2,000 feet long at the least. I'd make the runway wide enough to handle larger transport planes like the C-130 because you'd need to bring in a lot more suppies than can be handled by the C-2 Greyhound. As a point of reference, there actually were flight tests back in 1963 where a C-130E made repeated takeoffs and landings on the USS Forrestal. The tests were successful but there was so little clearance between the plane's wingtips and the superstructure that the idea was dropped.

Building such a monster ship would be expensive and difficult enough. Providing logistics support would also be a challenge. Larger planes like the AWACS, B-2, and Joint Stars will have to remain land-based and depend on refueling to reach the combat area.