FracSym: Automated symbolic computation of Lie symmetries of fractional differential equations

Jefferson, G.F., and Carminati, J. (2014) FracSym: Automated symbolic computation of Lie symmetries of fractional differential equations. Computer Physics Communications, 185 (1). pp. 430-441.

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In this paper, we present an algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs) using the method as described by Buckwar & Luchko (1998) and Gazizov, Kasatkin & Lukashchuk (2007, 2009, 2011). The method has been generalised here to allow for the determination of symmetries for FDEs with n independent variables and for systems of partial FDEs. The algorithm has been implemented in the new MAPLE package FracSym (Jefferson and Carminati 2013) which uses routines from the MAPLE symmetry packages DESOLVII (Vu, Jefferson and Carminati, 2012) and ASP (Jefferson and Carminati, 2013). We introduce FracSym by investigating the symmetries of a number of FDEs; specific forms of any arbitrary functions, which may extend the symmetry algebras, are also determined. For each of the FDEs discussed, selected invariant solutions are then presented.

Item ID: 77711
Item Type: Article (Research - C1)
ISSN: 1879-2944
Keywords: Fractional differential equations, Invariant solutions, Lie symmetry method, Symbolic computation
Copyright Information: © 2013 Elsevier B.V. All rights reserved.
Date Deposited: 28 Nov 2023 23:25
FoR Codes: 49 MATHEMATICAL SCIENCES > 4903 Numerical and computational mathematics > 490303 Numerical solution of differential and integral equations @ 100%
SEO Codes: 28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280118 Expanding knowledge in the mathematical sciences @ 100%
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