  The paper deals with a fractional derivative introduced by means of the
Fourier transform. The explicit form of the kernel of general derivative
operator acting on the functions analytic on a curve in complex plane is
deduced and the correspondence with some well known approaches is shown. In
particular, it is shown how the uniqueness of the operation depends on the
derivative order type (integer, rational, irrational, complex) and the number
of poles of considered function in the complex plane.
