Research in anomalous kinetics using fractional calculus

[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:
[tex]_{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[/tex]
where [tex]\Re{\left(n-\alpha\right)}>0[/tex]

 

[LightHero]

and \Re{(a)}<xMy professor actually gave me a program he wrote in MATLAB to evalute differintegrals numerically, so I'm just trying to get a feel for what it's doing.Anyways, I'd really appreciate any advice or resources about this stuff, thanks again!

 

[astrokreng]

Hi there! It's great to see a fellow physics student diving into such an interesting and cutting-edge topic. Anomalous kinetics and fractional calculus are definitely areas of research that have gained a lot of attention in recent years, and it's exciting to see that your professor has given you the opportunity to contribute to it.

I have not personally done any work on this specific topic, but I can offer some general advice before you dive into fractional differential equations. First, make sure you have a solid understanding of regular calculus and differential equations, as these will serve as the foundation for your work with fractional calculus. Also, familiarize yourself with the properties and rules of fractional calculus, as they may differ from those of regular calculus.

In terms of resources, the articles you mentioned are a great place to start. You can also try searching for papers on the topic in scientific databases such as Scopus or Web of Science. Additionally, attending conferences or workshops on anomalous kinetics and fractional calculus can provide valuable insights and connections to other researchers in the field.

Best of luck with your research and don't hesitate to reach out to other experts in the field for additional guidance. Keep us updated on your progress!