The Kushan Empire  was a syncretic empire, formed by the Yuezhi, in the Bactrian territories in the early 1st century. It spread to encompass much of modern-day territory of Uzbekistan, Afghanistan, Pakistan and Northern India. The Sasanian or Sassanid Empire officially known as Eranshahr  was the last Iranian empire before the early Muslim conquests of the 7th–8th centuries AD. Named after the House of Sasan, it endured for over four centuries, from 224 to 651 AD, making it the longest-lived Persian imperial dynasty.[
What's the relation between the Kushan Empire and the Sassanid Empire in Iran?
Kushano-Sasanian Kingdom (also called Kushanshahs,  or Koshano Shao in Bactrian, or Indo-Sasanians) is a historiographic term used by modern scholars to refer to a branch of the Sasanian Persians who established their rule in Bactria during the 3rd and 4th centuries CE at the expense of the declining Kushans. They captured the provinces of Sogdiana, Bactria and Gandhara from the Kushans in 225 CE. The Sasanians established governors for the Sasanian Empire, who minted their own coinage and took the title of Kushanshas, i.e. "Kings of the Kushans". They are sometimes considered as forming a "sub-kingdom" inside the Sassanid Empire.