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On the generalized time fractional reaction–diffusion equation: Lie symmetries, exact solutions and conservation laws

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  • Yu, Jicheng
  • Feng, Yuqiang

Abstract

In this paper, Lie symmetry analysis method is applied to the generalized time fractional reaction–diffusion equation. We obtain a conditional symmetric group and some conservation laws of the governing equation. The obtained Lie symmetries are used to reduce the studied fractional partial differential equation to some fractional ordinary differential equations with Riemann–Liouville fractional derivative or Erdélyi-Kober fractional derivative. Furthermore, we obtained asymptotic stable solutions and convergent power series solutions for the reduced equations. The dynamic behavior of these exact solutions is presented graphically.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924004077
    DOI: 10.1016/j.chaos.2024.114855
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    References listed on IDEAS

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    1. 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).
    2. Momani, Shaher & Odibat, Zaid, 2007. "Numerical comparison of methods for solving linear differential equations of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1248-1255.
    3. Jicheng Yu & Yuqiang Feng & Xianjia Wang, 2022. "Lie symmetry analysis and exact solutions of time fractional Black–Scholes equation," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 9(04), pages 1-17, December.
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