Final answer:
The Umayyad Dynasty was the powerful Arab empire that controlled much of Mesopotamia after Alexander the Great's empire fell.
Step-by-step explanation:
The powerful Arab empire which ruled over much of Mesopotamia after the collapse of the empire of Alexander the Great was the Umayyad Dynasty. During the seventh and early eighth centuries, the Arab armies, riding on their swift horses and camels and committed to their cause, conquered large territories in the Middle East, North Africa, the Iberian Peninsula, and Central Asia.
The Umayyad Dynasty ruled after a period of civil wars and religious unification wars across Arabia and the Middle East. They succeeded the remaining Byzantine and Sassanid territories to form an empire that was larger than any before it, encompassing a vast and diverse realm.
Under leaders like Mu'awiya, who established his capital in Damascus, and his successor 'Abd al-Malik, who completed the Dome of the Rock, the Umayyads consolidated their rule and expanded their empire. However, their reign eventually came to an end when they were overthrown by the Abbasid Dynasty in the mid-8th century CE.