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Zbl 0932.58038
Buckwar, Evelyn; Luchko, Yuri
Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations. (English)
[J] J. Math. Anal. Appl. 227, No.1, 81-97 (1998). ISSN 0022-247X

For $\alpha \ge 1$, $D > 0$, the authors consider the linear fractional order differential equation $\partial^\alpha u/\partial t^\alpha = D \partial^2 u/\partial x^2$, in the sense of the Riemann-Liouville fractional calculus. Similarity solutions with respect to the scaling transformations are found to be functions of the invariant $z = x t^{-\alpha/2}$. For them an ordinary differential equation in the Erdelyi-Kober derivative is obtained. As the final result, the general scale-invariant solution is computed in terms of Wright and generalized Wright functions.
[Michael Marvan (Opava)]

MSC 2000:: *58J72 Correspondences and other transformation methods
26A33 Fractional derivatives and integrals (real functions)

Keywords: fractional diffusion-wave equation; scale-invariant solution; Riemann-Liouville fractional calculus; Erdelyi-Kober derivative; generalized Wright functions

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