TY - JOUR

T1 - Lie symmetry analysis of a class of time fractional nonlinear evolution systems

AU - Dorjgotov, Khongorzul

AU - Ochiai, Hiroyuki

AU - Zunderiya, Uuganbayar

N1 - Funding Information:
We are very grateful to an anonymous referee for valuable suggestions and comments. We were able to improve the content of the work by addressing the points raised by the referee. This work was supported by JSPS (KAKENHI Grant No. 15H03613 ) and by the Foundation of Science and Technology of Mongolia (Grant No. SSA-012/2016).

PY - 2018/7/15

Y1 - 2018/7/15

N2 - 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.

AB - 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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U2 - 10.1016/j.amc.2018.01.056

DO - 10.1016/j.amc.2018.01.056

M3 - Article

AN - SCOPUS:85042176743

VL - 329

SP - 105

EP - 117

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -