- #1

- 7

- 0

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter deepurple
- Start date

- #1

- 7

- 0

- #2

- 483

- 2

Welcome to PF forums deepurple.

I hope people'll take the time to respond.

- #3

- 49

- 0

Hello. As far as I know there is no geometric interpretation for a derivative of fractional order.

- #4

- 59

- 0

Hello. As far as I know there is no geometric interpretation for a derivative of fractional order.

It turns out that for every power of fractional derivative there is a fractal function whose fractional derivative at that order is a constant, equal to the fractal dimension of the curve!

By a fractal function I mean a Weistrauss type continuous function that is nowhere differentiable in the traditional sense and which has a non-integer dimension in the sense of Hausdorf.

Incidentally fractional-calculus should be called non-integer calculus, since the index of the differential operator can be any complex value! A further generalization is possible by considering functions of the differential operator that cannot be represented as polynomials, i.e. F(d/dx), the most common of which is exp(d/dx), which acts as translation by one unit on real-valued functions:

[tex]e^{\frac{d}{dx}}f(x) = f(x + 1) [/tex]

I always vote for this one to go on the t-shirts instead of e^{i pi} + 1 = 0.

- #5

- 49

- 0

It turns out that for every power of fractional derivative there is a fractal function whose fractional derivative at that order is a constant, equal to the fractal dimension of the curve!

Wow. I would never have imagined that fractals and fractional (or 'complex order') calculus have anything to do. It's quite interesting.

- #6

- 713

- 5

Hello,

I know this thread is very old, but perhaps http://www.maa.org/joma/Volume7/Podlubny/GIFI.html" might provide useful information related to geometric interpretations of fractional integration/derivative to anyone coming upon this page.

I know this thread is very old, but perhaps http://www.maa.org/joma/Volume7/Podlubny/GIFI.html" might provide useful information related to geometric interpretations of fractional integration/derivative to anyone coming upon this page.

Last edited by a moderator:

Share: