Can we Define a Basis on R^3 at Every Point Using Fractional Derivatives?

[Klaus_Hoffmann]

Let be y=f(x) a differentiable function, my question is if we can define a basis on R^3 at every point using \partial _{x}^{n} n=0,1,2

For arbitrary 'n' even real numbers could be the same be defined using the fractional derivative to justify \partial _{x} ^{n} y(x)

So in every case the Wrosnkian is different from 0 except at several points, with this a possible purpose would be constructing a basis for a fractional-dimensional space to perform integration over R^{n} n being (positive) integer or real.

 

[matt grime]

A basis of what on R^3? (you wouldn't be the famous Klaus Hoffmann, musician and mellotron connosieur, would you?)