I'm guessing the Falleen Fed is the faction you are in? If so, then it is likely they can't help you as its unlikely they own it.
So far you haven't given us any information about this. How old is your character? Did you play before, get picked up/were flying around, then go inactive, and now come back after some period of time? If so do you remember who owned the ship from back then? If you are really new, then you should remember who came to pick you up, or who made you pilot of the ship.
And with these cases it is best to contact either the person that was one of the above, or make a post in the Traders Lounge with information above and the name and ID of the ship you are in. Then people can help you.