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Lie symmetry analysis and exact solutions of the time-fractional biological population model

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  • Zhang, Zhi-Yong
  • Li, Guo-Fang

Abstract

We first perform a complete Lie symmetry classification for the time-fractional biological population model with Riemann–Liouville fractional derivative and then construct the corresponding reduced equations with the obtained Lie symmetries. Moreover, with the F-expansion method and the reduced equations, we obtain several new exact solutions for the equation and show the propagation pattern via the evolutional figures. By means of the power series theory, an exact power series solution of the equation is also constructed.

Suggested Citation

  • Zhang, Zhi-Yong & Li, Guo-Fang, 2020. "Lie symmetry analysis and exact solutions of the time-fractional biological population model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    • Handle: RePEc:eee:phsmap:v:540:y:2020:i:c:s0378437119317662
    DOI: 10.1016/j.physa.2019.123134
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    References listed on IDEAS

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    1. Guo, Tian Liang & Zhang, KanJian, 2015. "Impulsive fractional partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 581-590.
    2. Huang, Qing & Zhdanov, Renat, 2014. "Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann–Liouville derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 110-118.
    3. Inc, Mustafa & Yusuf, Abdullahi & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Time-fractional Cahn–Allen and time-fractional Klein–Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 94-106.
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    Cited by:

    1. Yu, Jicheng & Feng, Yuqiang, 2024. "On the generalized time fractional reaction–diffusion equation: Lie symmetries, exact solutions and conservation laws," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    2. Andronikos Paliathanasis & Genly Leon & Peter G. L. Leach, 2022. "Lie Symmetry Classification and Qualitative Analysis for the Fourth-Order Schrödinger Equation," Mathematics, MDPI, vol. 10(17), pages 1-15, September.

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