## continuation of the “n-th derivative” function [closed]

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.

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## closed as no longer relevant by Qfwfq, Bill Johnson, Ryan Budney, Andres Caicedo, Andy PutmanJan 23 2012 at 3:20

I think you are looking for something like this: http://en.wikipedia.org/wiki/Fractional_derivative

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 that's exactly what i was thinking about! i never knew such thing existed. thanks a lot – alberto.bosia Jan 22 2012 at 9:22