Talk:Initialized fractional calculus

This page looks like an earlier draft of initialization of the differintegrals (which links here). Suggest merge.

Charles Matthews 12:09, 14 Oct 2003 (UTC)

that's only tentative. there is actually a lot more to discuss, and the literature generally puts it under the title of "initialized fractional calculus". by the literature, i'm refering mostly to the ressearch papers from NASA's John Glenn Research Center. These papers discuss such things as laplace transforms of fractional differintegral equations. That's what this space is "reserved" for. However, I seem to be about the only one working on this set of pages (just take a look at the page histories) So I'm constantly hoping at least one other person will start work on these pages with me. this is just an opportunity for that.

But that does not discuss the topic of organization that you brought up with your suggestion for merger. However, the topic of organization is the point of my contention in regards to my "loneliness" on these pages: Organization should be decided democratically; should be emerged or synergized. It might be better to make a section on "laplace transforming initialized differintegrals", or something of the sort. Who knows? Definitely not one person.

Part of the problem is, not only are there multiple methods of differintegration (which can all be brought into harmony via initialization), there are different schools of thought regarding the problem that fractional differintegration is not localizable. primarily two schools, the "local fractional derivative" and the "initialized fractional calculus". in fact, the LFD school has a different definition of d^qe^x and the other simple functions, which have correction terms. This is because the lower bound of the differintegral is assumed to start at zero instead of negative infinity. So do i make two separate laplace transfom sections? it creates a problem of organization. I'm compelled to think i should split it like the split in tensor calculus between the classical and modern treatment. But it's not exactly like that - there are more overlaps, and at the same time they are shifted because they're initialized differently (LFD is designed intentionally to avoid the problem of initialization).

In any case, thanks for editing these pages, I appreciate the contribution.

Kevin Baas

I'm only just starting in on the literature on this. In the classic Zygmund Trigonometric Series, the Weyl differintegral is used: but only for periodic functions, with integral = 0 over a period. Do you want to claim this definition in the general case?

Charles Matthews 09:15, 15 Oct 2003 (UTC)

I don't understand the question. I haven't seen Zygmund Trigonometric Series.

I think for the general case it's best to use an "improper differintegral" (i've never actually seen that phrase before) i.e. over the region negative infinity to infinity. And in general, whatever keeps things the simplest. But like I said, there are multiple differintegrals and multiple "schools". The special property of the Weyl differintegral is just it's region of integration. I think it might be best to make a separate page for each differintegral and go into the details about the uses and behaviors of them there, with focus on the fact that it is not the "differintegral" per se that leads to these phenomena, but the region of integration.

I don't know if that answers your question. Let me know if it helps.

(btw, the NASA papers I was refering to are linked on the Fractional calculus page. I found these very readable.)

-Kevin Baas

This is seriously poor...

I'm very sorry, but this page is so badly written that there is simply no hope of anyone understanding anything from it... (apart from the writer and references?)

I could present a long list of complaints, but all of them would amount to the same thing: "what is this sentence trying to say??", for almost every sentence. Firstly it doesn't even say what the topic is, it trails off into "an oddity" about the differintegral (composition property?), followed by an obscure example dribbling on without saying anything helpful... Finally, when it reaches the end, it still doesn't even say what the topic is about, only that "Working with a properly initialized differintegral is the subject of initialized fractional calculus".

I tried to rewrite the bad prose, but without understanding the subject. It needs an expert. M∧Ŝc²ħεИ_τlk 21:48, 5 March 2013 (UTC)

Proposal for the Addition of Information on Fractional Operators

Considering the following references:

Acceleration of the order of convergence of a family of fractional fixed-point methods and its implementation in the solution of a nonlinear algebraic system related to hybrid solar receivers

Sets of Fractional Operators and Numerical Estimation of the Order of Convergence of a Family of Fractional Fixed-Point Methods

Would it be possible to add the following information on fractional operators?

<<Lengthy copy and paste trimmed>> Calfracsets (talk) 06:27, 12 August 2024 (UTC) Calfracsets (talk) 16:12, 5 September 2024 (UTC)

No. Please stop spamming this stuff all over Wikipedia - this is not a place for you to promote yourself or your original theories. MrOllie (talk) 16:16, 5 September 2024 (UTC)

At least you have already read the works and the works of other authors that are derived from them?

Because this page seems to do exactly what you mention that it cannot be done.

https://en.wikipedia.org/wiki/Initialized_fractional_calculus

and I don't see any problem in sharing new information already confirmed by other authors. Calfracsets (talk) 16:24, 5 September 2024 (UTC)

This article is not in great shape, but the material appears to have been covered in a Springer yellow book. Feel free to nominate it for deletion if you disagree that it is a notable topic. Russ Woodroofe (talk) 10:36, 6 September 2024 (UTC)

References