I can't tell if the ends are black, or if they are feathery. But it resembles what I've seen my boy do. If it is tail biting (or fin biting, they aren't fussy), then clean water is what will be best. I've added a bit of stress coat after I've discovered a tail biting incident, just to help heal and prevent infection. I'm pretty sure tail biting if left untreated can turn into fin rot.
Also, high protein diet, my boy is getting fed frozen blood worms once a day. He loves them. While live foods would be best, lets face it, not available to everyone. Frozen is a decent alternative, and it's fairly affordable. The hardest part is being willing to work with frozen blood worms.
Good luck, and keep up with the clean water! Oh, as a side note, my Scuzi loves his floating plants (live). I was suggested to try some live plants to help with his biting tendencies.