Talk:Fractional calculus

1/gamma

Article currently notes in multiple places that gamma is “undefined” on negative integers. In fact, it has a very well defined value, the complex infinity. Indeed, 1/gamma is that rarest of creatures, an entire analytic function (with well defined value = 0 at the negative integers, of course).

Presently, there is a “dubious - discuss” note at one of these places, so I am not the first reader to question the wording. Is there any reason not to scrap this wording? Jmacwiki (talk) 23:51, 26 February 2022 (UTC)

Fixed, and the note about “dubious” removed. I’m still not enthusiastic about saying the particular changes of tactic for negative integers are “necessary” (I suspect there are many routes to the destination), but at least the statements about gamma are not inaccurate. Jmacwiki (talk) 02:25, 17 April 2022 (UTC)

Non-complex differential definitions only?

Some of the derivative explanations, such as “Riemann–Liouville fractional integral”, refer to expressions defined on intervals, with different definitions on different subintervals. It is not clear how to extend these to complex-valued paths, except possibly when the imaginary parts of the endpoints are equal.

Would the result be path-dependent (I hope not!), or does the definition just need a better exposition? (My situation: I know a LOT of basics, but I came here hoping to learn this material, not improve its explanation.) Jmacwiki (talk) 00:33, 27 February 2022 (UTC)

ambiguous "Fractional derivative of a basic power function" section hiding the most important formula

AFAIK (and understand from the text), the last part of this section starting with "For a general function f(x)" is really about any kind of f() and not only for f() being a basic power function, as expected by the section title.

Also, this general formula is probably the most important part of this page since it explain how to practically compute it (when you don't want to do it in Fourier or Laplace space ).

So I guess it should deserve its own paragraph. — Preceding unsigned comment added by Fabrice.Neyret (talk • contribs) 17:40, 9 May 2022 (UTC)

I take issue with this section, but not for the same reasons you do. This wording implies that this is the way of computing the fractional derivative of a power function, which it is not. There are many different fractional derivatives as detailed in the later in the page under "Fractional integrals" and "Fractional derivative" and they do not follow this form. As well as saying that was the general formula for fractional derivatives is also misleading if not false. The formula in this section is pretty much the same as the Riemann-Liouville fractional integral.

I do however think that it would make more sense if it were tweaked and moved as a "Special case of basic power functions" section in the Riemann–Liouville_integral article.

Same with the Laplace transform section. I think it can be moved the Riemann-Liouvile integral article as motivation for it's definition alongside the Cauchy repeated integral rule. Coffeevector (talk) 06:52, 2 September 2022 (UTC)

Which character does the article use for the index of differentiation?

The nice illustration with caption "The animation shows the derivative operator oscillating ..." appears to use a Greek lowercase alpha for the index, whereas the article appears to use a Roman lowercase A. (Unless my eyes are deceiving me.)

It's probably best if they both use the same character, especially because the caption does not define the meaning of that character but assumes it is understood. 2601:200:C000:1A0:9D6A:3426:156B:13FB (talk) 23:36, 17 June 2022 (UTC)

Two equivalent definitions of Caputo fractional derivative

There seem to be two equivalent definitions given of the Caputo fractional derivative, one using α and one using ν, which is confusing. One of them should be removed. Since α seems to be used consistently throughout the article, I would suggest removing the definition that uses ν. Some editing of the surrounding text will also be required. Benjamin Rich (talk) 15:10, 22 December 2023 (UTC)