Fictional, fictive, and fictitious all branch off the "fiction" tree, but fictional is literary, fictive is specific, and fictitious is just plain fake.
The word fictional is like "pretend" with a literary bent. Jay Gatsby is a fictional character. Novels, short stories, and plays are fictional, or made-up, but there are also fictional TV shows and movies. Examples of the word:
"The author has come under fire for equating Navajo religious beliefs with the world of her fictional Harry Potter characters." (National Geographic)
"As President Frank Underwood on 'House of Cards,' Kevin Spacey is deft at playing fictional presidents." (Washington Times)
The less common word fictive describes a specific thing created by the imagination. Your pets might be your fictive audience when you practice for the talent show. If you call your dad's best friend your uncle, that's a fictive kinship — there's a little invention. Fictive in action:
"The children were then told that the adults didn't have time to distribute the rest of their stickers to other kids in a fictive class." (Science Magazine)
"I can't claim any fictive kinship here — I only met him for a couple hours." (Los Angeles Times)
Anything fictitious is also made up, but often with trickery in mind. If you tell the coffee barista that your name is Picklehead Sunshine, then you gave a fictitious name. (Unless you're reading this, Pickles.) In The Talented Mr. Ripley, Tom takes on a fictitious identity when he pretends to be Dickie, a man he murdered. Other examples:
"She said she signed a fictitious contract with the company but never worked for them." (BBC)
"Authorities say the suspects opened accounts online by pairing real Social Security numbers with fictitious names and birth dates." (Washington Times)
These three words love fiction but each in its own way. Fictional loves books and plays, fictive loves the imagination, and fictitious loves lies!