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<p>In this paper, our focus is on the (2+1)-dimensional mixed fractional Boiti-Leon-Manna-Pempinelli equation (MFBLMPE), which incorporates a Riemann–Liouville time fractional derivative alongside an integer-order derivative in the y-direction. The model can be used to simulate the process of water propagation. The exact solutions to the MFBLMPE are constructed through the distinct application of Lie symmetry analysis and the invariant subspace method. Firstly, the Lie algebras admitted by the MFBLMPE are derived utilizing Lie symmetry analysis. Subsequently, a corresponding one-dimensional optimal system is established, followed by the execution of symmetry reduction. Furthermore, conservation laws are derived using the newly formulated Noether theorem. Ultimately, Matlab is employed to visualize the three-dimensional diagrams of certain obtained solutions.</p>

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Symmetry Analysis and Application of the Invariant Subspace Method to the (2+1)-dimensional Mixed Fractional Boiti-Leon-Manna-Pempinelli Equation

  • 期刊论文

  • 发表日期：

    2026年2月13日

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  • Yapeng Shi,
  • Yuqiang Feng,
  • Jicheng Yu

摘要

In this paper, our focus is on the (2+1)-dimensional mixed fractional Boiti-Leon-Manna-Pempinelli equation (MFBLMPE), which incorporates a Riemann–Liouville time fractional derivative alongside an integer-order derivative in the y-direction. The model can be used to simulate the process of water propagation. The exact solutions to the MFBLMPE are constructed through the distinct application of Lie symmetry analysis and the invariant subspace method. Firstly, the Lie algebras admitted by the MFBLMPE are derived utilizing Lie symmetry analysis. Subsequently, a corresponding one-dimensional optimal system is established, followed by the execution of symmetry reduction. Furthermore, conservation laws are derived using the newly formulated Noether theorem. Ultimately, Matlab is employed to visualize the three-dimensional diagrams of certain obtained solutions.