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
Available: Pr-A-98-01.ps
Contact: Evelyn Buckwar, Yurii Luchko, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, 14195 Berlin, Germany (luchko@math.fu-berlin.de)
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