Can someone explain fractional calculus?

[jack476]

So, apparently, it's possible to generalize integration and derivation into non-integer orders. For instance, it's apparently possible to take the 0.5th derivative of a function.

What I'm wondering is what would be represented by such an equation? If a derivative represents how a function changes over time, like velocity and acceleration, what on Earth would you do with the fractional derivative?

Here's the Wikipedia page (http://en.wikipedia.org/wiki/Fractional_calculus) just to make clear I'm not confusing it with partial derivatives, which by this point I'm well acquainted with :P

 

[jedishrfu]

A very interesting article, I had never heard of fractional calculus before. I look at this as mathematicians investigating an area for their own curiosity not that it applied to anything practical. The graphics show how varying the fractional power gets you curves between the function and its derivative which is cool in and of itself. They even describe using complex powers also pretty cool.

At the very end of the article, the author outlines the uses in acoustics, quantum mechanics, fluid flow and diffusion all valid applications. Now I'm going to have ask around about it at work. Thanks.

 

[jack476]

A very interesting article, I had never heard of fractional calculus before. I look at this as mathematicians investigating an area for their own curiosity not that it applied to anything practical. The graphics show how varying the fractional power gets you curves between the function and its derivative which is cool in and of itself. They even describe using complex powers also pretty cool.

At the very end of the article, the author outlines the uses in acoustics, quantum mechanics, fluid flow and diffusion all valid applications. Now I'm going to have ask around about it at work. Thanks.

You're quite welcome. After you've asked your coworkers could you please let me know what they had to say (since from the sound of it you work around a lot of math people)? I tried reading the article but it seems to be well above my understanding.

 

[jedishrfu]

You're quite welcome. After you've asked your coworkers could you please let me know what they had to say (since from the sound of it you work around a lot of math people)? I tried reading the article but it seems to be well above my understanding.

Mine too.

 

[1MileCrash]

One of the professors at my school has this as a main part of her research (looking at her publications, it appears frequently in the form of fractional differential equations). I've never done much reading into it, and it's well beyond my knowledge as well, but the example in the Wiki article of the monomial x^k is at least quite simple to follow. It looks like they noted the general pattern for the nth derivative (natural n) of x^k, which involves factorials, and then changed the domain of this pattern to the reals by replacing factorials with the gamma function, and shows that it satisfies the desired properties of the idea of an rth derivative.