My knowledge of fractional calculus is very limited. But from what I understand, the general defintion of the nth derivative of a function f(x) (a defintion that is inexplicably not given in most calculus textbooks)

can be extended to derivatives of non-integer order by use of the generalized binomial theorem

Even though this seems like a logical extension to make, and expected results occurs (e.g., ) is there a geometric interpretation of fractional derivatives?

Also, is it correct to say that integration is then just a specific type of differentiation?