Here’s a fractional fillomino. Please excuse the lazy rendering, I don’t expect to make more of these.
Rules Subdivide the grid into areas. Numbers within an area must equal the size (in unit squares) of that area. Areas of the same size must not touch along an edge.
Maybe Puzzles 
I must be missing something…
Isn’t the “1” region in the top right already 3/2 units?
There’s a bit of a meta aspect to this puzzle. It’s more fractional than just allowing half squares.
Oh, fun! Although I see why you don’t expect to be making another one of these, as they don’t really work with different square divisions now.
Weird when starting, but fun once I found some rules which made sense. Thanks!