Answer:
Il-Khan dynasty.
Step-by-step explanation:
The dynasty that went by the name of Il-Khan ruled the western part of the Mongol Empire. Hulagu Khan, who was the grandson of the Great Khan and the founder of the Khanate, exercised the power over this territory, although it was officially subjected to Genghis Khan.
At the end of the 13th century, the rules of Ilkhanate converted to Islam. The present-day city of Baghdad was located west, at the empire's very border.