I would urge interested readers to hunt down Robert Silverberg's beautifully written short story "Lion Time in Timbuctoo". It has a 20th Century CE dominated by Muslim Turks, Africans, Incas, Aztecs, and various Asian powers due to the Black Plague killing three-quarters of the European population rather than the 1/4 or 1/3 that died in reality.
Greater Timbuktoo during the 14th and 16th Centuries CE was an very sophisticated culture with some kickass metallurgy that attracted trade and savants from all over the nascent Islamic world while Europe was stuck in a plague-ridden feudal Hell. I mean c'mon, during the Dark Ages the best they came up with was the windmill and a really cool new horse collar. Okay, there was Francis Bacon, John Jay and a coupla other sharp cats. The Renaissance could have gone a completely different way by a few missed shipments or different whispers in various courtly ears.
Anyone interested in Silverberg's "Lion Time in Timbuctoo" can find it and other wonderful Alternative History stories in Martin Greenburg's The Way It Wasn't: Great Science Fiction Stories of Alternative History 1996, Citadel Twilight (screw Amazon, go to abebooks.com). Out of print I'm sure, but really worth worth hunting down. It has several wonderful stories from such greats as Howard Waldrop's "Ike at the Mike", Fritz Leiber, Gregor Benford, Pamela Sargent, and Barry M. Malzberg. Also included is "The Winterberry" by Nicholas A. Dichardo about a reality where JFK survived that horrible day in Dallas. If you can read that without shedding a tear check yourself into the nearest mausoleum; 'cuz sibling, you have no soul. Just lay down and stop breathing.
By the bye, that Silverberg story is also available in Tor Books Beyond the Gates of the Worlds 1991.