I'll take a stab.
The ottomans sit out WW1, focus on strengthening & liberalizing(modernizing) their society.
In Europe 'proper' WW1 get's set off largely on cue, but proceeds differently - due to various butterflies, the end result is a series of xenophobic military/monarchial dictatorships, lightly sprinkled with revanchist demagogues and totalitarian communist rebellions from Russia (the butterflies weren't enough to derail that portion of OTL).
For next couple of decades, Europe remains a divided armed camp, fighting various skirmishes with shifting alliances. The Ottomans continue to develop, becoming a primary trade partner for the US (which also sat out the European War) and the various ex-colonial states (constant warfare & high states of readiness gradually bankrupted the core imperial states, combined with the increasing reluctance of the colonials to get slaughtered in the various metropoles' pointless bloodletting, a series of successful independence movements kicked off at various points, resulting in a largely decolonized world slightly in advance of OTL).
By the later 20th century (1970-1980) the Ottoman Imperial Republic, Nippon, China, Brazil, the United States of America, Argentina, Chile, Australia, India, and Malaysia are the wealthiest and most advanced nations of the world.
Europe is a squalid, squabbling, repressed backwater, just beginning to break away from 4 generations of intercenine slaughter.