Precomp the layers that compose the part of the image to be faded on the right and left sides. On this precomp, use a full-screen rectangular mask with a horizontal-only feather on it. Adjust the right and left sides of the mask. Increase/decrease the amount of feather to taste. Done.
Dave's method is great.
Like all things AE, there are many ways to accomplish the same thing.
Some alternatives are: Make a black & white gradient ramp on one layer, and use it for a track matte on another matte. You can also use the Set Matte effect to copy the alpha of one layer to another.
There are direct ways to create alpha ramps using 3rd party plug-ins like Ramp Alpha that's in Red Giant's Key Correct and Image Lounge.
Here, I'll throw in another solution. Use the a shape layer filled with a gradient for:
a. A track matte
b. your lower third artwork
c. the source for a Silhouette alpha blend mode
I seldom use Effect>Generate>Ramp any more. I use Shape layers filled with a gradient you can use a bunch of colors, you can use transparency, you can stack up gradients and blend them.