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.

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  Reply With Quote

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.  Reply With Quote

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.  Reply With Quote

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  Reply With Quote

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.  Reply With Quote

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.  Reply With Quote

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"...).  Reply With Quote

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.  Reply With Quote

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.  Reply With Quote

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  Reply With Quote

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