ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 45, 26, 33 Buckwar, Evelyn, Luchko, Yurii, Dept. of Mathematics and Computer Science, Freie Universitaet Berlin, Arnimallee 2-6, 14195 Berlin Application of the Lie group of scaling transformations to the fractional diffusion-wave equation In this talk a symmetry group of scaling transformations is determined for the fractional diffusion-wave equation of order α, containing among particular cases the diffusion equation and the wave equation. For its groupinvariant solutions an ordinary differential equation of fractional order with the new independent variable z = xt^{−α/2} is derived. The derivative then is an Erdelyi-Kober derivative depending on a parameter α and its solution is given in terms of generalized Wright functions. The connection with the well-known results in the case of derivatives of integer order will also be presented.