Evelyn Buckwar, Yuri Luchko,
"Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations"
, in Journal of Mathematical Analysis and Applications, Vol. 227, Nummer 1, Elsevier, San Diego, CA, Seite(n) 81-97, 1998, ISSN: 0022-247X
Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations
Sprache des Titels:
In this article a symmetry group of scaling transformations is determined for a partial differential equation of fractional order ?, 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 variablez = xt ? ?/2is derived. The derivative then is an Erdelyi?Kober derivative depending on a parameter ?. Its complete solution is given in terms of the Wright and the generalized Wright functions.