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

Jefferson, G.F.; Carminati, John

doi:10.1016/j.cpc.2013.09.019

Cited by 60 publications

(36 citation statements)

References 15 publications

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“…which is identical to that obtained in [17] for m = 1 2 and k = 1. Note that (20) is invariant under the transformations corresponding to X 2 and X 4 .…”

Section: Reduced System Of Odes Corresponding To U 5 In Case 21supporting

confidence: 88%

Lie symmetry analysis of a class of time fractional nonlinear evolution systems

Dorjgotov

Ochiai

Zunderiya

2018

Applied Mathematics and Computation

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We study a class of nonlinear evolution systems of time fractional partial differential equations using Lie symmetry analysis. We obtain not only infinitesimal symmetries but also a complete group classification and a classification of group invariant solutions of this class of systems. We find that the class of systems of differential equations studied is naturally divided into two cases on the basis of the type of a function that they contain. In each case, the dimension of the Lie algebra generated by the infinitesimal symmetries is greater than 2, and for this reason we present the structures and one-dimensional optimal systems of these Lie algebras. The reduced systems corresponding to the optimal systems are also obtained. Explicit group invariant solutions are found for particular cases.

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“…which is identical to that obtained in [17] for m = 1 2 and k = 1. Note that (20) is invariant under the transformations corresponding to X 2 and X 4 .…”

Section: Reduced System Of Odes Corresponding To U 5 In Case 21supporting

confidence: 88%

Lie symmetry analysis of a class of time fractional nonlinear evolution systems

Dorjgotov

Ochiai

Zunderiya

2018

Applied Mathematics and Computation

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“…We see that the explicit expression for the above ones can be obtained in a standard procedure [31]. In addition, according to [40], after similar calculation as [35], we can have the explicit expression for φ α,t :…”

Section: Preliminariesmentioning

confidence: 90%

“…Because we will use FracSym [40] in our paper, as request, hereafter, we only consider symmetries where φ is linear in u (assume µ α t = 0), i.e.,…”

Section: Preliminariesmentioning

confidence: 99%

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Lie Symmetry Analysis and Exact Solutions of Generalized Fractional Zakharov-Kuznetsov Equations

Zhang

2019

Symmetry

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This paper considers the Lie symmetry analysis of a class of fractional Zakharov-Kuznetsov equations. We systematically show the procedure to obtain the Lie point symmetries for the equation. Accordingly, we study the vector fields of this equation. Meantime, the symmetry reductions of this equation are performed. Finally, by employing the obtained symmetry properties, we can get some new exact solutions to this fractional Zakharov-Kuznetsov equation.

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“…Our works [8], [9], [10], [11], [12] illustrate the symmetry search procedure based on infinitesimal approach and the possibility of invariant solution construction using different admitted operators. This approach was successfully used to investigate different FDEs [13], [14] and even to create the software package for automatic symmetry computation [15].…”

Section: Introductionmentioning

confidence: 99%