I agree with J.R. and have upvoted his answer. The adjectives "fictitious" and "fictional" are hands-down far more common in English than "fictive", but all three of these words are interrelated. The adjective "fictional" is often used regarding a story that is not real; it is merely made up or contrived. A Christmas Carol by Charles Dickens is a fictional story. A person who lies about where he was during a certain time has told a fictional account of his whereabouts.
"Fictitious" is usually used for something that is made up in order to deceive another person. A criminal can use a fictitious name to deceive others. This is where the overlap between "fictional" and "fictitious" exists because the example regarding a person who lies about his whereabouts for a certain time has not only given a fictional account of his whereabouts, but he has also given a fictitious account of his whereabouts. Furthermore, definition no. 2 on freedictionary.com also states that the adjective "fictitious" means "[o]f or relating to the characters, settings, or plots that are created for a work of fiction." Its example includes this:
"[A] book in which fictitious characters interact with historical
The adjective "fictive" can also mean "fictional", but it's far less common than "fictional". Your definition above, "created by the imagination", is one of the definitions of "fictive". It can be used in senses of being very creative with the imagination:
"His imagination has all of the fictive qualities. At night, he even
counts sheep jumping over his bed."
The use of "fictive", however, is very rare in English because we have better words like "imaginative" in this sense and "fictional" in the other sense of the word's meaning: "of or relating to fiction." The most prominent use of the word "fictive" in English is definition no. 3 on freedictionary.com: "[r]elating to or being a kinship-like relationship among people who are not related by heredity, marriage, or adoption, often involving the use of kinship terms." An example of this is when children call their mother's best female friend their "aunt":
"Our mother's friend, Aunt Crystal, is not really our aunt; it's a
fictive title. We call her that because she's so close to our mother personally that it's as if she were our mother's sister."
I hope that might have helped you out. Take care and good luck!