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al-Hasani
Arabs didn't ruled over Turks as a people, they only used kidnapped children as slaves, I think these are vastly different things.
Ottomans didn't bothered to fully conquer everywhere they had control over, even in Anatolia they had small vassalships, it had many reasons, such as not bothering conquer loyal tribal groups as it had almost no benefits, or region being too far/hard to effectively control.
It was Islam they had adopted, unfortunately in the past, people associated Arabic culture with Islam which is degenerated many cultures, I think a similar thing applies to Christianity as well. Persians and Persian culture/language was more valued and looked after in the Ottoman empire and other Islamic Turkic states, foreign official in state service were largely Persians, Persian history/mythology was valued, while Arabic influence was mostly about religious/judicary affairs, Persian influence was in literature, poetry etc., in fact we could say Arabs were not perceived so positive or praised in Ottoman empire.