So first things first, this is not a fan fiction. It is a fan theory. If you have a problem with that you can stop reading now. After giving it some thought I think I have found out the story behind Alfendi and how he exist if Claire, the only one the Professor loved, is dead. So without further ado my fan theory.
When you think about it this way Alfendi's life makes sense. Claire was pregnant with Layton's child, Alfendi, of course, and did not tell him. She was pregnant during the times of the time travel experiments. So when she was sent 10 years into the future she had lived with her son Alfendi for a little less than 10 years. It take a normal pregnancy takes 38 weeks and there are about 52 weeks in a single year. So keeping that in mind he was around 9 or 10 during the events of the Unwound Future game. Layton never knew about his son, and when Claire really died it was a traumatic experience for the young child. After doing some research I found out that a traumatic experience can cause a multiple personality disorder. That would explain the Potty Prof. Now he says he has a brother He was left with no one. But we never see him, and why would they use the word brothers the title it if there are no brothers? Well, I believe that Alfendi was left with no one to care for him when his mother, Claire, died. It is a way of explaining why he is so unorganized. He had no one to teach him. He says he has a brother to make it seem like he was raised with someone, when in fact he wasn't. He made his brother up so he could have hope that there was someone to care for him. Ever wonder why we never see his brother? That's why. In the games it is obvious that Alfendi knows about his father, Professor Layton, but it is also obvious that the Professor does not know about his son. The Professor would take care of his sone if he knew he had one, I mean that is what a true gentleman would do, correct? He couldn't take care of him though, because he never knew he had a son. Last thing, His multiple personality disorder. I already explained how he got it but his personalities represent his life. Alfendi is the one that made up the brother to stay hopeful and the Potty Prof is the one that gave up hope. As I see it the Potty Prof is sort of negative, as he is the hopeless one, while on the other hand, Alfendi is kind and caring, because he grew up without a kind caring person. He is trying to be what he grew up without.
Well, there you have it, my first fan theory. Hope you understood this and that it will make the games easier to understand.
PM me with any questions. See ya!