The three do have some similarities, and sometimes are used interchangeably. Of the three, fictive is the least common. Here are some areas that the words could be used a little more distinctly.
Fictional is the the word used mostly to talk about literary works to make a difference between biography/history, true crime, etc. Made up stories and characters are all fictional.
Fictitious is also made up, but it can be used to talk about something made up to deceive someone. Someone might hand in a fictitious resume when applying for a job. Something is not just "unreal"; it's false. A fictitious report might make the board of directors vote one way or another in a company. Someone can give police a fictitious name if they are stopped. In this case, people could say "fictional" but I think "fictitious" is more precise.
Fictive could be used in the other situations as well, but I've heard it used mostly for feelings that aren't true. Someone might have a fictive concern for his terminally ill colleague, but really he is hoping to take the colleague's job. A set phrase with fictive is "fictive kinship," a familial relationship that is "made up". I have a lot of students who will call someone "auntie" even though the two people are not related by blood or marriage. It could be people who were neighbors back in their home country and now they treat each other like aunts and nieces do.