OPERATOR OF FRACTIONAL DERIVATIVE IN THE COMPLEX-PLANE

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