I’m curious about the meaning, interpretation and defintion of fractional differentials. Google didn’t really help, and the only thing I found on here was this thread. (which I posted to 
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What is the meaning of these beasts? What “real world” interpretation can be applied to them, if any?
I know there are smart people reading this board that know something about this.
I don’t know anything about Fractional Derivatives, but this might help: Fractional Calculus.
If you’re really that interested, there are five cites at the bottom of the page, which also goes into Fractional Integration.
This is highly theoretical, so you won’t get any meaning or real-world interpretation out of it. The same site also gives the solution to one Fractional Differential Equation.