If you express your feelings and solve problems by talking rather than yelling, your message will be that much stronger. Your children will learn from watching you and listening to you. Conflicts are often more common when children are tired, bored or have spent too much time together. Providing quiet time, or private spaces where children can safely be by themselves, may help prevent conflicts. You do not have to treat children the same to be fair.
Children have different needs and different personalities.
For example, it's fair to allow older children to stay up later. It's fair to give younger children some extra attention when they're tired. It's fair to give shy children extra praise when they try something new. Often siblings will try different activities as a way to show their individuality. If you encourage children to build their special talents, they will have less need to compete.