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

Lie symmetry analysis of a class of time fractional nonlinear evolution systems 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Computation Elsevier

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

Applied Mathematics and Computation, Volume 329 – Jul 15, 2018
13 pages

/lp/elsevier/lie-symmetry-analysis-of-a-class-of-time-fractional-nonlinear-d8VJXc6s6c
Publisher
Elsevier
ISSN
0096-3003
eISSN
1873-5649
D.O.I.
10.1016/j.amc.2018.01.056
Publisher site
See Article on Publisher Site

### 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.

### Journal

Applied Mathematics and ComputationElsevier

Published: Jul 15, 2018

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