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 Ufimsk. Mat. Zh., 2012, Volume 4, Issue 1, Pages 71–81 (Mi ufa134)

Symmetry properties for systems of two ordinary fractional difeferential equations

A. A. Kasatkin

Ufa State Aviation Technical University, Ufa, Russia

Abstract: Lie point symmetries of two systems of ordinary fractional differential equations with the Riemann–Liouville derivatives are considered. Infinite algebra $L$ of equivalence transformation operators is constructed. It is shown that all admitted operators generate some subalgebra in $L$ and classification of systems with respect to point symmetries can be based on the optimal system of subalgebras. The optimal system of one-dimensional $L$ subalgebras and the complete normalized optimal system for its finite-dimensional part $L_6$ are constructed.

Keywords: fractional derivatives, symmetries, group classification, optimal system of subalgebras.

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Citation: A. A. Kasatkin, “Symmetry properties for systems of two ordinary fractional difeferential equations”, Ufimsk. Mat. Zh., 4:1 (2012), 71–81

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\Bibitem{Kas12} \by A.~A.~Kasatkin \paper Symmetry properties for systems of two ordinary fractional difeferential equations \jour Ufimsk. Mat. Zh. \yr 2012 \vol 4 \issue 1 \pages 71--81 \mathnet{http://mi.mathnet.ru/ufa134} 

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