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

Khongorzul Dorjgotov, Hiroyuki Ochiai and Uuganbayar Zunderiya

Applied Mathematics and Computation, 2018, vol. 329, issue C, 105-117

Abstract: 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.

Keywords: Fractional nonlinear system; Lie symmetry; Optimal system; Invariant solution (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:329:y:2018:i:c:p:105-117

DOI: 10.1016/j.amc.2018.01.056

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