I was curious if anyone could give me an example of the use of fractional derivatives in physics and explain what they offer that "conventional" mathematics does not (in terms of new physics and not just another method to work the problem)?
If you look at the conservation of mass example on the wikipedia page they cite the paper http://www.stt.msu.edu/~mcubed/fcom.pdf they derive a general equation for conservation of mass in equation 13. It seems like the fractional derivative is then used as a method to approach their problem, but I dont think it includes new physics (correct me if I'm wrong on this). Is there anything gained by stating that fractional conservation of mass holds in this case (apart from gaining another way to approach the problem)?
Any thoughts on this example or others would be appreciated!