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Symmetry 2019, 11(1), 77; https://doi.org/10.3390/sym11010077

Some Exact Solutions and Conservation Laws of the Coupled Time-Fractional Boussinesq-Burgers System

1
School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
2
State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China
*
Author to whom correspondence should be addressed.
Received: 25 December 2018 / Revised: 5 January 2019 / Accepted: 7 January 2019 / Published: 11 January 2019
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Abstract

In this paper, we investigate the invariant properties of the coupled time-fractional Boussinesq-Burgers system. The coupled time-fractional Boussinesq-Burgers system is established to study the fluid flow in the power system and describe the propagation of shallow water waves. Firstly, the Lie symmetry analysis method is used to consider the Lie point symmetry, similarity transformation. Using the obtained symmetries, then the coupled time-fractional Boussinesq-Burgers system is reduced to nonlinear fractional ordinary differential equations (FODEs), with E r d e ´ l y i - K o b e r fractional differential operator. Secondly, we solve the reduced system of FODEs by using a power series expansion method. Meanwhile, the convergence of the power series solution is analyzed. Thirdly, by using the new conservation theorem, the conservation laws of the coupled time-fractional Boussinesq-Burgers system is constructed. In particular, the presentation of the numerical simulations of q-homotopy analysis method of coupled time fractional Boussinesq-Burgers system is dedicated. View Full-Text
Keywords: coupled time-fractional Boussinesq-Burgers system; Lie symmetry analysis; symmetry reduction; explicit solutions; conservation laws coupled time-fractional Boussinesq-Burgers system; Lie symmetry analysis; symmetry reduction; explicit solutions; conservation laws
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Shi, D.; Zhang, Y.; Liu, W.; Liu, J. Some Exact Solutions and Conservation Laws of the Coupled Time-Fractional Boussinesq-Burgers System. Symmetry 2019, 11, 77.

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