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There is the first derivative \(\dfrac{d}{dx}\)

and there is the second derivative \(\dfrac{d^2}{dx^2}f(x)=\dfrac{d}{dx}(\dfrac{d}{dx}(f(x)))\)

I wonder if there is something like a one third derivative?

Something like:

\(\dfrac{d^{1/3}}{dx^{1/3}}\)

\(\dfrac{d^{\sqrt2}}{dx^{\sqrt2}}\)

Or even:

\(\dfrac{d^{\pi}}{dx^{\pi}}\)

Or

\(\dfrac{d^{e}}{dx^{e}}\)

Even crazier:

\(\dfrac{d^{1+\sqrt3 i}}{dx^{1+\sqrt{3}i}}\)

I wonder if those things exists?

MaxWong  Jun 30, 2017
 #1
avatar+27035 
+3

Have a look at http://www.mathpages.com/home/kmath616/kmath616.htm, or do a more general search for "fractional calculus".

Alan  Jun 30, 2017

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