Are you referring to equivalents in the Islamic period or something else? If you can narrow down to a specific period, it would definitely help us to give you a thorough answer.

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Assuming you're referring to the Islamic Middle East, some well-known and common titles of status that could be compared to European noble titles such as Count, Duke, Earl, King, et cetera would include the Sultan, Emir, Sheikh (this word typically denoting an elder or leader of a local-level community, though not necessarily a ruler in his own right.) Sharif, And Sayyid. One thing to note about some of these titles (not unlike the case for European noble titles across realms) is that there is no universally established hierarchy throughout and after the Islamic period and some of these titles have been taken by rulers more or less powerful than each other - rulers using the title of "emir" or "amir" have been subordinate to other rulers and emirs also have ruled as independent sovereigns of their realm. Popularly, however, the title of "Emir" typically denotes an Islamic provincial leader (someone who rules over a region that constitutes a larger realm or state) at the very least nominally subordinate to some higher authority (see: United Arab Emirates, and usage during the Caliphates.)

This situation is comparable to the European titles of "duke" and "count," some of whom, such as the counts of Anjou, Blois, and Flanders, operated with relative autonomy and significant political influence around the period of the high middle ages, despite being subjects to a higher authority (in this case, the King of France.)

Trying to get some sources for further reading together, but if you're interested in some insight on interactions between nobles and their liege, the sections on 12th-13th century France in Western Warfare in the Age of the Crusades, 1000-1300 by John France are a good read.