Yes, in 117 AD, Trajan invaded a part of Iraq, the Parthian Empire then: They lost it in 119 AD. read more
At times of war, when successful, Roman control expanded beyond that river (several Roman emperors sacked Ctesiphon/Susa/Pasargade, capitals of the Parthian/Persian empires). Trajan conquered all of what is today Iraq, but his successor Hadrian gave it back and put the border back at the river. read more
Roman Parthia. Romans were able to conquer the westernmost part of Parthia under emperor Trajan. Indeed, in 113 AD Trajan invaded Parthia, marching first on Armenia. In 114 AD Trajan annexed Armenia to the Roman empire, after defeating and killing Parthamasiris, relative of Osroes I of Parthia. read more
Mesopotamia was the name of two distinct Roman provinces, the one a short-lived creation of the Roman Emperor Trajan in 116–117 and the other established by Emperor Septimius Severus in ca. 198, which ranged between the Roman and the Sassanid empires, until the Muslim conquests of the 7th century. read more