It could possibly be fin rot, the fins do sometimes look "melty" when they get fin rot.. See what others have to say. Has his behaviour changed in anyway? Fill out this form it'll be useful:
If it is fin rot you can add 1tsp of AQ salt to his water to the gallon for five days with 100% water changes everyday. If he improves and you see new growth you can remove the salt. If it is still there then use salt for 5 more days but no more than that. You can do this in your current tank setup as long as you don't have any live plants or snails.. Otherwise use a quarantine tank.