Howdy, isn't this a simple matter of feathering the edge of an object(s) Effect > Stylize > Feather?

You also used a Gradient Mesh here's a tute for that...
http://layersmagazine.com/adobe-illustrator-gradient-mesh-tool.html

And, you could also try using an Opacity Mask...
http://creativetechs.com/tipsblog/transparent-gradients-in-illustrator/

Edge feathering mini tute...
http://help.adobe.com/en_US/Illustrator/14.0/WS714a382cdf7d304e7e07d0100...

Good luck, hope that helps.

5star, thanks a lot for your your info. It was very useful.

5star, I looked at all the links, tried to do the effect, but haven't had any luck. Can you please tell me step by step how you did it?

Show us the results of your efforts so far, and describe step-by-step how you arrived at it.

It'll be easier for us to see which part you might need help with.

I first used the blue gradient, then feathered. After that I applied the extrude and bevel, but I can't get it to have a thicker edge.

I don't know if that's the way 5star did it.
Thanks.

Forget extrude and bevel. Just one flat object with a gradient under a copy of the object with a slightly different gradient and a feathered edge. No stroke or other effects on either object.

Thanks Luma Vine, now I understand how 5star did it. I tried it and it works great. But after playing around a while I managed to do it with the 3D Extrude and Bevel options, expanding, compounding path, deleting... I forgot how, ha ha. Gonna try and do it again. This time I'll write it down.
Thanks for everything guys.