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<p>In this paper, the nonlinear fractional differential equation with variable coefficients, the fractional Riccati–Bernoulli equation, is considered. Based on the Lie symmetry analysis theory, the invariant solutions and the exact solutions of the fractional Riccati–Bernoulli equation are obtained under certain parameter conditions, which widely promote the relevant conclusions in existing literature. The results show that Lie symmetry analysis method is effective for solving the fractional Riccati–Bernoulli equation.</p>

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Lie symmetry analysis and solutions for a fractional Riccati–Bernoulli equation

  • 期刊论文

  • 发表日期：

    2025年5月7日

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  • Shaoru Liu,
  • Yanxia Hu

摘要

In this paper, the nonlinear fractional differential equation with variable coefficients, the fractional Riccati–Bernoulli equation, is considered. Based on the Lie symmetry analysis theory, the invariant solutions and the exact solutions of the fractional Riccati–Bernoulli equation are obtained under certain parameter conditions, which widely promote the relevant conclusions in existing literature. The results show that Lie symmetry analysis method is effective for solving the fractional Riccati–Bernoulli equation.