lets break this down please :

Finally, since we can write (w - z)--1 = e(-a-1)(log (w-z)) and log is a multivalued function, we will take the real part of the logarithm when w - z > 0. We arrive at the following definition: Definition 4.1. Let f(z) = >Pg(2), where g(2) is analytic on a simply con- nected domain D C 2 C C : 0 ED, and let Re(p) > -1. Then we define the Fractional Derivative of order a of f(z) (denoted Do f (z) ) as f (@) ( 2 ) = Daf ( 2 ) = r(a +1) f(w) (w - z)at1 dw (5) o for a * -1, -2, -3