Reddening at the base of the fins is most commonly caused by an ulcerative disease/hemorrhagic septicemia. This is generally caused by the bacteria aeromonas, pseudomonas, and vibrio.
Reddening of the vent is commonly seen as well, so try to get a look at that. Keep an eye out for any apparent ulcers/sores/lesions on the body.
You can try some antibacterial medicated fish food as long as he is eating. Feed this to the other fish as well, as these bacteria can spread to other healthy fish. If he stops eating, he needs to be quarantined and treated with something like KanaPlex.
If ulcers appear, you can treat them topically with something like Bio Bandage.
These bacteria are present at very low levels in any fish, but only become a problem when some source of stress or decreased immune system occurs. Most commonly this is caused by bad water quality, overcrowding, etc. This doesn't seem to be the case with your aquarium, so it may be a decreasing immune system in an older fish.