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).
Publisher Copyright:
© 2018 Elsevier Inc.
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
SN - 0096-3003
VL - 329
SP - 105
EP - 117
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -