a carrier that carries one fighter

rather useless and impractical

Since both would be flying you could probably design a way to land that isn't the same as that used for an aircraft carrier. Depending on how fast the zeppelin could go it might be similar to process of refueling in air.

Then again, I don't know the minimum airspeed a F22 remains controllable at. You could always resort to Harrier like planes to make it less of an issue.

Why build a billion dollar air ship that one $1000 missle could take out....

With current technology we could probably build one on the moon, put it in orbit, and it could deploy space planes.

Aircraft stay in the air under two principles...

Thrust and Lift.

Our fighter jets use Thrust to stay aloft, although the F-22 can maneuver at near zero air speed, if the pilot is good enough. That, however, is completely different than landing! Right now most aircraft hit the deck of a carrier around ~160 Mph, and then are arrested to a full stop in about 2 seconds with the tail hook and cable system on the carrier. Which brings up another point....

The cable arrest system on a carrier is massive, and not just a simple cable. It also has to be able to withstand the forces of a ~55,0000 pound aircraft doing ~160 mph. Zeps aren't structurally sound enough to withstand these forces, they are simply skeletons. If you took a cable arrest system off a carrier and put it on a Zep, it would just rip the Zep apart.

So the only possible way to bring a plane to a relative stop over a small area is a cable arrest system? It is impossible to have two bodies meet up at similar airspeeds and require much less force in making one of the bodies come to a relative stop?

You want to have the aircraft carry move at over 200 mph?

Fire? Its just exhaust fumes that comes out after the ignited fuel has been burned forcing the expanded gas to propel the craft. Its a jet, not a rocket

Except you now need a fuselage filled with helium capable of withstanding such airspeeds. Which the weight of the material exceeds your bouyancy. There is a good reason why they make dirigible skins out of cloth you know.

A solid fuselage would also add quite a bit of weight. The 747 without its wing and interior is close to 130 metric tons. Which only gets around 1600 m3 of internal volume or around .8 tons of buoyancy.

Meaning you would be getting nowhere as your fuselage is over 100 times heavier than the bouyancy you get from your helium.

More like a zeppelin doing half that