A Fractional spacetime, dimension equation

[jk22]

Suppose we use fractional derivatives (https://en.m.wikipedia.org/wiki/Fractional_calculus) in GR, hence we have a local group symmetry $SO(3-\epsilon,1+\epsilon)$ does any reference exist about an equation for $\epsilon$ ?, since it could depend on coordinates too.

 

[jambaugh]

Woah there Tex! Fractional derivatives is one thing (a purely algebraic concept). Fractional dimensions is another (ah la fractal geometry). But I don't think you can sensibly talks about fractional dimension parameters for Lie groups such as SO(p,n). If you wish to then you need to go into the lengthy coherent exposition of exactly what you mean but that, including explaining whether you're still even talking about a group much less a Lie group.