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Consider a fractional integral or derivative, what can we associate to them in geometrical or physical terms, I have seen that for fractional derivatives the greater the order of derivative the less area that a right angle triangle encloses at certain point, but what would happen with a fractional integral, and also what is the significance of $\frac{d^i f(x)}{dx^i}$ or in general of $\frac{d^{a+bi} f(x)}{dx^{a+bi}}$.

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  • $\begingroup$ There is no physical interpretation and everything I've seen including the triangle area thing are extremely contrived and artificial. It's best, at least currently, to think of it as an integral transform, and heuristically think of the kernel as something that weights certain parts of the function more than others. Also this is a duplicate ;) $\endgroup$ – Zach466920 Jun 12 '15 at 22:00
  • $\begingroup$ I knew I wasn't the only one with that doubt, so where is the original? $\endgroup$ – transistorNPN Jun 13 '15 at 1:41
  • $\begingroup$ Go to the tags page on this site. Type in fractional calculus. There'll be multiple questions discussing the above. Also some other interesting easter eggs discussing applications ;) $\endgroup$ – Zach466920 Jun 13 '15 at 3:11

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