The Caliphate of Cairo
Abbasid Caliphate.
The first Caliph Abou Bakr, then Omar. then Othman, then Aly
The Umayyad dynasty was a great Muslin dynasty that ruled the empire of the Caliphate.
The capital of the Rightly-Guided Caliphate was MEDINAduring the reigns of Abu Bakr, 'Omar, and 'Othman. They used the infrastructure left over from when Muhammad had ruled the Islamic Polity from Medina. However, when 'Ali took power, he felt that he needed to put his capital in the Upper Middle East, so he moved it to KUFA. After 'Ali's death, the Rightly-Guided Caliphate was abolished by the Umayyads.
Abu Bakr ruled over the Rashidun Caliphate from 632-634 CE when he became the first Muslim Caliph following Muhammad's death.
I think the term you are looking for is caliphate, and the ruler was called a caliph.
Umayyad Dynasty
The Fatimid Caliphate, an Islamic caliphate ruled by the Fatimid dynasty, was the Muslim power in Jerusalem before the First Crusade. They controlled Jerusalem and its surrounding territories in the 10th and 11th centuries.
Cronus ruled over the titans.
North India (ruled by Lodhi) and Rajputana (ruled by Rana Sanga)
In theory at least, most of north Africa was ruled by the Ottoman Empire.