From your photo...which are excellent...it looks like fin rot to me which is a bacterial infection limited to the fin, but, can extend to the caudal peduncle. I didn't see any spots on the body, so, I am assuming it is not ich.
Fin rot is caused by stress, usually poor water quality....you didn't mention any of your water parameters? Without treatment, the rot may progress. Usually it is a gram negative bacteria, aeromonas, eg. Isolation in a hospital tank if the fish is not alone, water changes, aquarium salt and a tetracycline based AB would be the way to go.SH