This Golden Age wasn't strictly Muslim either. The Umayyad and early 'Abbasid states, as well as the Umayyad splinter state in Cordoba and the Fatimids in Egypt experienced it, but so did their neighbor to the north. All of these regions heavily traded with one another...but there was no common thread. Since it's convenient to ignore the Byzantine revival that occurred at the same time as the primarily 'Abbasid Golden Age (and which was still going strong by the time the Cordoba caliphate splintered into taifas, fwiw), and instead label that empire as "moribund" and "in decline", the ninth-century Mediterranean period of flowering culture is ascribed primarily to the Muslim (or Arab, depending on who you talk to) political entities involved.This Golden Age wasn't strictly Arab though. The various Arab dynasties, as well as the North African Fatimid and the Spanish Ummayad Dynasties all experienced this golden age, as did the Ottomans. All of these regions heavily traded with one another and all were linked by a common thread - Islam.
FWIW, the Ottoman period of greatness had basically nothing to do with the 'Abbasid-centered golden age, being separated by centuries of comparative decay, by the standards of those who describe history in such terms.