Use a layer mask on the edited top layer.

In GIMP, add a mask to the top layer and initialize it to white. Then paint or apply a black-to-white gradient on the mask:

• white on the mask = the top layer stays visible
• black on the mask = the top layer becomes transparent
• gray = partial transparency

So if you want the effect to taper off gradually, draw a gradient on the mask in the direction you want the fade. This lets the original image on the lower layer show through smoothly.

A layer mask is usually better than editing the alpha directly because it is easy to adjust later without permanently changing the layer.