1. ## Quick question about fractional derivatives and is Latex broken?

Assume generalized binomial coefficients. Also assume this is not for normal fractional (iterative) derivatives, but for the following operation. I think I should implement it in python or something... just wonder if there is an easy way to do it on a phone (like how do I code it for Wolfram Alpha???) since my computer time is limited.

Latex broken? I specifically prohibit Bilby from replying to this part of the question if no forum user is wearing latex.

$f^n(x) = \lim_{h \to 0} \frac{ \sum\limits_{k=0}^\infty \binom{\alpha}{k} (-1)^k f(x+ (n-k) h ) } {h^n}$

So, limits as h-->0:
f0 (x) = [f(x) ]/h^0
f1 (x) = [f(x+1h) - f(x) ]/h^1
f1.5 (x) = [f(x+1.5h) - 1.5 f(x+.5h) + 3/8 f(x-.5h) +1/16 f(x-1.5h) +3/128 f(x-2.5h).... ]/h^1.5
f2 (x) = [f(x+2h) -2 f(x+h) +f(x) ]/h^2
f3 (x) = [f(x+3h) -3 f(x+2h) +3 f(x+h) -f(x) ]/h^3

2. I don't think your formula work at all.

https://en.wikipedia.org/wiki/Fractional_calculus
Unlike integer, fractional derivative in general is not even local.

3. I am not familiar with the term fractional derivative, can you explain?

There are several free tools. Euler is a good one. They all have scripted languages to write code. They are all straightforward.

You can do it in a spreadsheet with Basic. Open Office is free and has basic with the spreadsheet.

4. Originally Posted by steve_bank
I am not familiar with the term fractional derivative, can you explain?
https://en.wikipedia.org/wiki/Fractional_calculus

5. One other thing. Get a programmable TI or HP calculator. They have always had a serial, link to a PC. They may connect to a wireless device. Edit and download programs. Even without that you can program iterative solutions. Used them often before PCs.

6. Originally Posted by barbos
I don't think your formula work at all.
Apparently it does. <shrug>

https://www.mathpages.com/home/kmath616/kmath616.htm

Originally Posted by barbos
https://en.wikipedia.org/wiki/Fractional_calculus
Unlike integer, fractional derivative in general is not even local.
As far as I can tell, from what I just read (and it makes perfect sense to me), no derivative is local, because the derivative of any constant is 0.

Thanks barbos.

7. Originally Posted by steve_bank
I am not familiar with the term fractional derivative, can you explain?
Try when I get back. Limited computer time.

lol. I still see your name as steve_bnk, without the a. I think of you as that too (I read "Steve Be En Kay"...).

8. Originally Posted by Kharakov
Originally Posted by barbos
I don't think your formula work at all.
Apparently it does. <shrug>

https://www.mathpages.com/home/kmath616/kmath616.htm
OK, I stand corrected. But I need to read it more. Easiest/most natural way to calculate or think of fractional derivative is through Fourier transformation.

Originally Posted by barbos
https://en.wikipedia.org/wiki/Fractional_calculus
Unlike integer, fractional derivative in general is not even local.
As far as I can tell, from what I just read (and it makes perfect sense to me), no derivative is local, because the derivative of any constant is 0.

Thanks barbos.
Ordinary non-fractional derivatives are local: depend only of function behavior near argument. Fractional derivatives involves integration, so they depend on the boundaries and therefore not local.

9. So, I'm just basing this off of what I read in that article, which makes sense to me.

No derivative is local. The derivative of x^2 + 1000000000 = the derivative of x^2 - 159-8135907125309710298098510970912537097 = the derivative of x^2.

10. Originally Posted by Kharakov
So, I'm just basing this off of what I read in that article, which makes sense to me.

No derivative is local. The derivative of x^2 + 1000000000 = the derivative of x^2 - 159-8135907125309710298098510970912537097 = the derivative of x^2.
.
That has nothing to do with locality

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