Operator of fractional derivative in the complex plane

Details Operator of fractional derivative in the complex plane Operator of fractional derivative in the complex plane

1996-08-12

arxiv.org/abs/funct-an/9608002v2

Commun.Math.Phys. 192 (1998) 261-285

Mathematics

Functional Analysis

30 pages, Tex, 10 PostScript figures. This slightly compressed version will appear in Comm. in Math. Phys

Scientific paper

10.1007/s002200050299

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.

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