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

Jefferson,GF and Carminati,J 2014, FracSym: automated symbolic computation of Lie symmetries of fractional differential equations, Computer physics communications, vol. 185, no. 1, pp. 430-441, doi: 10.1016/j.cpc.2013.09.019.

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Title FracSym: automated symbolic computation of Lie symmetries of fractional differential equations
Author(s) Jefferson,GF
Journal name Computer physics communications
Volume number 185
Issue number 1
Start page 430
End page 441
Publisher Elsevier BV
Place of publication Amsterdam, Netherlands
Publication date 2014-01
ISSN 0010-4655
Keyword(s) Fractional differential equations
Invariant solutions
Lie symmetry method
Symbolic computation
Science & Technology
Physical Sciences
Computer Science, Interdisciplinary Applications
Physics, Mathematical
Computer Science
Summary 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. © 2013 Elsevier B.V. All rights reserved.
Language eng
DOI 10.1016/j.cpc.2013.09.019
Field of Research 010504 Mathematical Aspects of General Relativity
010207 Theoretical and Applied Mechanics
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2014, Elsevier BV
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Document type: Journal Article
Collection: School of Information Technology
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