The main conflict in "Bud, Not Buddy" by Christopher Paul Curtis is Bud's circumstances after the death of his mother when he is left in the care of the state. He lives with an abusive family in a foster home until he runs away to look for the man he believes is his father, and eventually finds him.
In this story, Bud is an orphan who loses his only parent (his mother) at the age of 6. He eventually winds up with an abusive foster family. His foster brother Todd bullies him multiple times, which makes him think of running away. Bud feels he isn't where he belongs, so he packs his bags and goes out searching for his father.
Bud believes Herman E. Calloway is his father, who is the guy that he has seen in pictures on the music posters he got from his mother's house. But, in order to find him, he needs some help. Therefore, he tries to find the nice librarian, Miss Hill, so he can ask her for help, but finds out that she has just gotten married and left town.
The conflict is resolved when Bud, who is still on the run, uses all the hints and things his mother told him about throughout the journey and finds a way to Grand Rapids, where he meets Herman E. Calloway and is accused of robbery. Bud shouts the name of his mother (Angela) when he is being accused of stealing, revealing he is actually Calloway's grandson. Bud finds this out when Mr. Jimmy, who is Calloway's band member, tells him that Angela Janet is Herman E. Calloway's daughter's name. Bud finally finds a home with his grandfather.