### 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.

Original language | English |
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Pages (from-to) | 105-117 |

Number of pages | 13 |

Journal | Applied Mathematics and Computation |

Volume | 329 |

DOIs | |

Publication status | Published - Jul 15 2018 |

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### All Science Journal Classification (ASJC) codes

- Computational Mathematics
- Applied Mathematics

### Cite this

*Applied Mathematics and Computation*,

*329*, 105-117. https://doi.org/10.1016/j.amc.2018.01.056

**Lie symmetry analysis of a class of time fractional nonlinear evolution systems.** / Dorjgotov, Khongorzul; Ochiai, Hiroyuki; Zunderiya, Uuganbayar.

Research output: Contribution to journal › Article

*Applied Mathematics and Computation*, vol. 329, pp. 105-117. https://doi.org/10.1016/j.amc.2018.01.056

}

TY - JOUR

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

AU - Dorjgotov, Khongorzul

AU - Ochiai, Hiroyuki

AU - Zunderiya, Uuganbayar

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.

UR - http://www.scopus.com/inward/record.url?scp=85042176743&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042176743&partnerID=8YFLogxK

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 -