Preprint No. A-98-01

Evelyn Buckwar, Yurii Luchko

Invariance of a partial differential equation of fractional order under a certain Lie group

Abstract: In this article a symmetry group of scaling transformations is determined for a partial differential equation of fractional order $\alpha$, containing among particular cases the diffusion equation, the wave equation, and the fractional diffusion-wave equation. For its group-invariant solutions an ordinary differential equation of fractional order with the new independent variable $z=xt^{-\alpha/2}$ is derived. The derivative then is an Erdelyi-Kober derivative depending on a parameter $\alpha$. Its complete solution is given in terms of generalized Wright functions.

Keywords: Fractional diffusion-wave equation, group-invariant solutions, Erdelyi-Kober derivative, generalized Wright function

Mathematics Subject Classification (MSC91): 45K05 Integro-partial differential equations , 45J05 Integro-ordinary differential equations

Language: ENG


Contact: Evelyn Buckwar, Yurii Luchko, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, 14195 Berlin, Germany (

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