Noein: To Your Other Self(2005)

Noein: Mou Hitori no Kimi e

In the near future, a violent battle takes place between the dimension La'cryma (protector of humanity) and the dimension Shangri-La, bent on the annihilation of all space-time. A group known as the Dragon Calvary is dispatched through space and time, searching for the only thing that can stop the invasion: the Dragon's Torque.

In the present, twelve-year old Haruka and her friend Yuu, are contemplating running away from home when they meet a member of the Dragon Calvary named Karasu (Crow). He believes that Haruka possesses the Dragon's Torque and claims to be Yuu from fifteen years in the future...

(Source: DVD Complete Series Box Set)