Hi Alex, if you want it to gradually fade, use the magic wand tool ( ) to select the black border, then click the gradiant tool ( ). Now choose the style of gradiant, i would say your best bet would be a circular one ( ). Now you change the box that looks like this : :AllColorChannels: , to this: :AlphaChannel: simply by clicking it.
Now you are all set, just left click the center of the image and gradually drag your mouse to the outer parts, this will make your boarder gradually fade.
If you want the whole border to be nearly transparent just lower the transparency by double clicking the layer and setting it to a lower setting*
*the boarder would need to be on a different layer