Musaigen no Phantom World

The story takes place in the near future, in a world born of human imagination. What humans would call ghosts or monsters appear, and they come to be called "phantoms." The main character, Haruhiko Ichijō, is a first year at Hosea Academy along with his upperclassman Mai Kawakami, who fights phantoms with the ability "Spirit of Five Elements," Izumi Reina, who has the ability "Phantom Eater," and Koito Minase, who fights phantoms in solitude. They experience the ups and downs of high school life before a certain incident leads them to the truth of this world.

(Source: Anime News Network)