I found a paper from Princeton called "Axiomatic Basis for Spaces with Non Integer Dimension" that presents five axioms and then starts to create a framework similar to what I'd think the subject would look like. However, a lot of questions are left unanswered.
I think this is more of a mathematical question than a physical question simply because the math isn't very well developed if at all, thus an physical questions regarding my question are irrelevant since there's nothing, at least currently, to study.
Is this a subject with a searchable name? If so, what are some good papers to read? (No paywalls please) Also, feel free to provide intuition for any, or all, of this :)