Fractional calculus - uses, examples?

[elegysix]

Does anyone know any applications / uses for fractional derivatives and integrals?

I supposed the idea and asked a professor, he tried to explain fractional calculus to me, but I was in calculus 2 at the time... so it was way over my head back then. I asked him what it could be used for and he didn't really give me an answer, just that it was too complex to explain lol.

Now, 3 years later, I'm looking back on it and wondering what a fractional derivative can be interpreted as, and what it could be used for. Anyone have some insight?

 

[pwsnafu]

Way too many to count. What interests you?

We have three specialized journals:

1. Fractional Calculus and Applied Analysis
2. Fractional Differential Equations
3. Communications in Fractional Calculus.

Of which the second is applications based.

I highly recommend Podlubny's book Fractional Differential Equations, or West's book Physics of Fractal Operators as they both have a chapter on applications. Also http://people.tuke.sk/igor.podlubny/fc_resources.html" is really good place to start.

 

[elegysix]

Thanks, I'll check those out.

I think asking how to use it is too broad of a question,
is there like a specific physics problem where you need to use it?

 

[JJacquelin]

Does anyone know any applications / uses for fractional derivatives and integrals?

I supposed the idea and asked a professor, he tried to explain fractional calculus to me, but I was in calculus 2 at the time... so it was way over my head back then. I asked him what it could be used for and he didn't really give me an answer, just that it was too complex to explain lol.

Now, 3 years later, I'm looking back on it and wondering what a fractional derivative can be interpreted as, and what it could be used for. Anyone have some insight?

Some references are provided page 5 in a paper written for general public "La dérivation fractionnaire" :
http://www.scribd.com/JJacquelin/documents
(Sorry, not translated yet).
There are a lot of applications for fractionnal calculus. One of them is the genertalization of the basic physical notions of Inductance, Resistance, Capacitance. A very useful generalization for the calculus of impedance of some electrical networks, especialy in case of presence of CPE in it (Constant Phase Element) :