# Fractional Calculus ? What?

## Main Question or Discussion Point

Fractional Calculus...? What?!?!

I came across this Wiki article a couple of days ago:

http://en.wikipedia.org/wiki/Fractional_calculus

As a student who just finished an undergrad major in math, the idea of a "fractional derivative" or "fractional integral" is mind blowing! Up until I read the article, I pretty much thought that the differential and integral operators were "fixed."

Let f:R -> R be a fcn.

Geometrically speaking, if the derivative of a fcn f at a point p in its domain is the rate of change of the fcn at that point and the integral of a fcn over an interval in the domain is the "area under the curve," how can I interpret the fractional derivative and fractional integral?

Hi ssayani87,

I have first of all to admit that I am not an expert in this topic. However when I posed the same question to myself I came across http://www.maa.org/joma/Volume7/Podlubny/GIFI.html" [Broken] that looked quite interesting.

Hopefully someone more competent than me here in PF will add more useful information.

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pwsnafu

Do a forum search and you will come across a couple of threads here.

Geometrically speaking, if the derivative of a fcn f at a point p in its domain is the rate of change of the fcn at that point and the integral of a fcn over an interval in the domain is the "area under the curve," how can I interpret the fractional derivative and fractional integral?
This is incorrect. The "rate of change at a point" is more the physical interpretation of the derivative. That's why velocity is defined as rate of change of position. The geometrical interpretation is "slope of the tangent at that point", and then we associate "rate of change" to that.

While I agree Podulbny's "shadows on the wall" is a good geometrical interpretation, still not a physical interpretation, which is what we want.

chiro