let $D\_{\mathbb N}$ be the standard "n-th derivative" function


is it possible to make a continuation of $D\_{\mathbb N}$ to non integer values?


i mean a function $D\_{\mathbb R}$ such that $D\_{\mathbb R}(x,f)=D\_{\mathbb N}(n,f)$ for all $x=n\in\mathbb N$


it should be something relevant, linear interpolation usually doesn't make any sense.



continuation of the "n-th derivative" function
I think you are looking for something like this: <http://en.wikipedia.org/wiki/Fractional_derivative>


