My younger son slaps his older brother when they fight, and makes him do what he wants. They're 15 and 17, is it my business or not?

I'm a single mother, and have two teenage sons. They've been very close all their lives, and they still are. But in the past year or so, my younger son Dan has taken on a more dominant role, and it's almost like his older brother has replaced him as the little brother. My eldest son will go to his younger brother to seek his approval, ask his advice, and even obey his instructions. My younger son will sometimes literally snap his fingers and say 'Liam, go get me a coke". And my older son will obey without hesitation.

That's okay with me, it's their relationship. But my concern is that when they get into an argument or when Liam makes a mistake, my younger son will punish him physically for it. Like when Liam dropped his brother's new iPhone, Dan slapped him across the face so hard you could hear his teeth chatter. Or when Liam called Dan's girlfriend a b*tch, Dan backhanded his face in front of me. In these cases, Liam will just stand there embarrassed, as if he deserved a slap for being a naughty child.

They're grown up boys now, should I say something or let them sort their relationship out themselves?

You absolutely should say something and stop this behaviour. Neither is grown up yet. They are still going through puberty and are exploring life including their limits. As a parent it's your job to help them see those limits and defend their limits if they are reached.

Your younger son has no business slapping anyone, not his brother or anyone. It's not acceptable behaviour and if he doesn't learn this it only will get worse. Nor does he gets to order people around, also not family. He needs to learn some respect in this regard and you are the best person to teach him this.

You also need to discuss this with your older son and help him learn to stand up for himself. He isn't his younger brothers slave and nor should he accept this type of behaviour. He has as many rights to be loved and respected as anyone and has no reason to think he's less valuable. By allowing this type of behaviour from your younger son your older son could get a different idea. You probably would not want this for him and as such you need to address it and preferably quickly.