Use the adjective fraternal to mean "brotherly," the way you'd describe your fraternal relationship with your oldest friend who is like a brother to you.
A fight between brothers? You could chalk it up to fraternal rivalry. Fraternal describes the relationship between brothers, but it is also used is to describe a club, society or fraternity, some brotherly group of people — usually men — with common interests. Fraternal twins, unlike identical twins, are formed from separate ova. That's why they don't look exactly alike and can be a girl and a boy, instead of two girls or two boys.