Communications in Mathematical Physics

, Volume 192, Issue 2, pp 261–285

Operator of Fractional Derivative in the Complex Plane

  • Petr Závada

DOI: 10.1007/s002200050299

Cite this article as:
Závada, P. Comm Math Phys (1998) 192: 261. doi:10.1007/s002200050299


The paper deals with a fractional derivative introduced by means of the Fourier transform. The explicit form of the kernel of the general derivative operator acting on the functions analytic on a curve in the 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 the considered function in the complex plane.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Petr Závada
    • 1
  1. 1.Institute of Physics, Academy of Sciences of Czech Republic, Na Slovance 2, CZ-180 40 Prague 8, Czech Republic. E-mail: zavada@fzu.czCZ