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# I wonder if...

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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?

Jun 30, 2017

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

Jun 30, 2017