INVARIANT ANALYSIS AND CONSERVATION LAWS FOR THE SPACE-TIME FRACTIONAL KDV-LIKE EQUATION

Jian-Gen Liu; Xiao-Jun Yang; Yi-Ying Feng; Lu-Lu Geng

doi:10.11948/20220202

2024 Volume 14 Issue 1

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Jian-Gen Liu, Xiao-Jun Yang, Yi-Ying Feng, Lu-Lu Geng. INVARIANT ANALYSIS AND CONSERVATION LAWS FOR THE SPACE-TIME FRACTIONAL KDV-LIKE EQUATION[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 1-15. doi: 10.11948/20220202

Citation:

Jian-Gen Liu, Xiao-Jun Yang, Yi-Ying Feng, Lu-Lu Geng. INVARIANT ANALYSIS AND CONSERVATION LAWS FOR THE SPACE-TIME FRACTIONAL KDV-LIKE EQUATION[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 1-15. doi: 10.11948/20220202

INVARIANT ANALYSIS AND CONSERVATION LAWS FOR THE SPACE-TIME FRACTIONAL KDV-LIKE EQUATION

1.
School of Mathematics and Statistics, Changshu Institute of Technology, Changshu 215500, Jiangsu, China
2.
School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China
3.
State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China
4.
School of Mathematics and Statistics, Suzhou University, Suzhou 234000, Anhui, China

Author Bio: Email: xjyangcumt@163.com(X.-J. Yang); Email: yyfeng12cumt@163.com(Y.-Y. Feng); Email: gengllcumt@163.com(L.-L. Geng)
Corresponding author: Email: ljgzr557@126.com(J.-G. Liu)

Abstract

Abstract

Fractional calculus plays an essential role in describing nonlinear phenomena appears in applied sciences. In this article, we handle mainly the Korteweg-de Vries (KdV)-like equation which can be used to depicted the shallow water waves evolution mechanism in the sense of the space-time fractional derivative of the Riemann-Liouville. Firstly, on the basis of the Lie symmetry analysis technology, the symmetry of this considered model was constructed. Then, this equation can be changed into a fractional ordinary differential equation with the help of the Erdélyi-Kober fractional operators. Subsequently, the one-parameter group of Lie point transformation and a special type exact solution of this researched model were also obtained. Lastly, based on the nonlinear self-adjointness, conservation laws of the space-time fractional KdV-like equation can be found. These results can provide us with a new scheme for studying space-time fractional differential equations.
- Invariant analysis /
- similarity reduction /
- one-parameter transformation lie group /
- nonlinear self-adjointness /
- conservation laws
MSC: 76Mxx, 70G65

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References

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