Looks like a bacterial fin rot to me, make sure your tank stays clean and try either an antibiotic laced food like the one made by JUNGLE, or adding some anti biotic to it's food (such as chloromycetin), as a last resort put it in a quarantine tank and treat the water there with a broad spectrum antibiotic like Maracyn-2, try not to use this in your main tank as it will kill off you filter bacteria. Any of these treatments will stop the infection and though it takes a while for the fins to heal completely they should show healthy tissue growth within 10 days of treatment. The small white spots sometimes persist as scarring after the disease has been cured but the edge fraying and rot will be gone.