Hello /sci/, are there any mathematical considerations which would define objects like $\mathbb{R}^{1/2}$ or $\mathbb{R}^{3/2}$? (I.e., considering $\mathbb{R}^n$ where $n \notin \mathbb{N}$.) If so, what field(s) is this studied in?

I've also heard that Leibniz considered stuff like the "halfth derivative" - e.g., if $f^{(1)}(x)$ is the first derivative and $f^{(2)}(x)$ is the second derivative, then he looked at how we might define $f^{(1/2)}(x)$ - but I'm not entirely sure about this either.

Links would be appreciated, as I have not been able to find much on Google. I'm guessing this is due to not knowing the actual vocabulary used to describe these things, if it even exists, but maybe I'm just an idiot lmao