Fractional Calculus

[Fermat]

Hey guys, I have a quite random question. So last week in class we were talking about calculus in my math class and my teacher mentioned that there is a field called fractional calculus (nothing we will cover but it's out there) and it made me wonder... What is one half derivative for example? It doesn't make much sense to me. If you think of derivatives as the slope of the tangent at a certain point, how can you then take half of a slope? And what use is it?

I have read about it on Wikipedia http://en.wikipedia.org/wiki/Fractional_calculus but it's still not clear to me. I know this is not a very common toppic but I was just wondering if anyone here knows a little more about it.

[Drake Glau]

Looks like it could be used for some much more intense integration than I've ever seen by changing the function into a series. Having the derivative be to a certain power can help to identify convergence or divergence letting you know the characteristics of the functions. Knowing this would give you the parameters that you can work in for certain processes of testing/integration.

That is my 11pm glance at wikipedia and coming up with some sort of bs for you

[aldld]

I haven't really read any of the actual theory of fractional calculus. But while doing some research for my EE, I ended up making a lot of use of the gamma function, which extends the domain of the factorial function. This led me to stumble upon a possible formula to generalize the power rule for a more general class of derivatives. It's easy to see that when k is an integer,

If you replace the factorials with the gamma function, you get

where n > -1 (can likely be generalized to other real values) and n - k > -1.

Then again, I haven't formally defined what it means when k is not an integer.

[Fermat]

Thanks for the help guys, I really appreciate it. Although it seems to just make things more complicated