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 Ichijo, 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)
Episode 1 - Age of Phantoms
Episode 2 - Take Out the Annoying UFO!
Episode 3 - Operation Copy-Paste Memories
Episode 4 - Fake Family
Episode 5 - I Can't Use My Special Abilities!
Episode 6 - Kurumi and the Teddy Bear Kingdom
Episode 7 - Schrödinger's Cat Mansion
Episode 8 - Break Through the Monkey Hot Spring!
Episode 9 - The Strange Tale of the Bakumatsu Phantom
Episode 10 - Little Ruru's Big Dream
Episode 11 - Tiny Haruhiko-kun
Episode 12 - The Mother Hath Returned
Episode 13 - The Eternal Phantom World