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I read from Leonard Mlodinow's Feynman's Rainbow that Feynman has defined the concept of a half-derivative, an operation $g$ on a function $f$ such that $$g(g(f))=f'.$$ I wonder if it is possible to develop a general rule of finding the half-derivative of any "half-differentiable" function just as finding the derivative of any differentiable function? Furthermore, can we generalize our answers to the previous questions to $\frac{1}{n}$-derivatives? Can we even defind irrational-derivatives?

Thanks in advance for any help.

Hyakutake
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    Did you have a look at https://en.wikipedia.org/wiki/Fractional_calculus and the various posts on this site? – Martin R Apr 17 '24 at 13:35
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    @MartinR You're too fast! I was just about to post the same link. :D Do note that there is a [tag:fractional-calculus] tag on this site, too. – Xander Henderson Apr 17 '24 at 13:37
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    There are different definitions of the fractional derivative. One important thing though is that they cannot be perfect i.e. their domain cannot cover constant functions w/o breaking the rule – ioveri Apr 17 '24 at 13:46

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