# Research in anomalous kinetics using fractional calculus

1. Jan 20, 2010

### gazebo_dude

Hi everyone, this is my first post on PF (yaay!). I hope this is in the right forum, if not I don't mind a mod moving this. I'm an undergrad physics student and one of my professors has hired me as a research worker over the summer break.

Has anyone here done any work on fractional calculus, anomalous kinetics, and/or electron transport through amorphous media? I've done a bit of lit review, but there is a lot of stuff out there. :) My prof gave me an article by Sokolov, Klafter, and Blumen (Nov 2002 issue of Physics Today) to start with, and I found a good review article by Metzler and Klafter (doi:10.1016/S0370-1573(00)00070-3). Anyone know of any particularly good resources?

So far I've mainly been getting practice applying the Riemann-Liouville differintegral to various different functions by power series, Laplace transforms, etc. Next my prof wants me to dive into some fractional differential equations. Any advice before I go headlong into it?

Thanks guys. I'm glad to be a part of PF.

The Riemann-Liouville differintegral is this beast:
$$_{a}D_{x}^{\alpha} f(x) = \left(\frac{d}{dx}\right)^n \frac{1}{\Gamma(n-\alpha)}\int_{a}^{x} \left( x - y \right)^{n-\alpha-1} f(y) dy$$
where $$\Re{\left(n-\alpha\right)}>0$$