There are a couple of alternative history sci-fi/fantasy series with this specific premise. It isn't one I'm really big on, so I don't remember the titles and authors at the moment, but I know they are out there.
If the Roman Empire had remained unified - and remained a powerful force - they would have needed to be content with a smaller Empire so they could defend themselves against the Goths and Visigoths, and they would not be stretched so thin all over the ancient world. And they would need to control Egypt.