First of all, just because he expanded the empire to its greatest size, Trajan does not qualify as a great conqueror. Second, Roman historians did not often go into great detail, and even when they did they were heavily censored by the emperors. Regardless, here's what I can find, by military campaign (of which he had only three):
1. Dacia: From Eutropius's "Brevium ab Urbe Condita":
"Trajan, after he had subdued Dacia, had transplanted thither an infinite number of men from the whole Roman world, to people the country and the cities; as the land had been exhausted of inhabitants in the long war maintained by Decebalus."
Key words here are "exhausted of inhabitants."
2. Nabataea: We still don't know what happened here.
3. Parthia: Trajan screwed up here and barely managed to accomplish anything before dying. He succeeded only in establishing a puppet ruler with little effort, violently suppressing rebellions, and establishing a few new provinces that Hadrian released from Roman control when he came to power.
To conclude, Trajan didn't do all that much, all of the histories talk about how he's a godly person, which is always a bit suspect, and of his three military campaigns, one left an area "exhausted of inhabitants," another is completely lacking in historical detail, and the last ended with those who accepted him living fine and those who didn't dead. All in all, not that much different than our friend Genghis, except that Genghis did a whole lot more.