Raphael was one of the reincarnated sons of Hamato Yoshi. During their mutation, Raphael was separated from his brothers, and spent a good portion of his early life alone. In fact, in the IDW incarnation, Raphael actually became friends with Casey Jones before he met his brothers.
In this incarnation, his rough, anger-prone personality has more reason, being bore from his time being alone on the streets. There, he had to fight to stay alive, and even after reuniting with his brothers, he is the most likely in a group to stick up for the underdog.
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History
The original Raphael (Mirage) first appeared Teenage Mutant Ninja Turtles: volume 1, issue #1.