Abstract In this paper, numerical solutions of space-fractional advection-diffusion equations, involving the Riemann-Liouville derivative with a nonlinear source term, are presented. We propose a procedure that combines the fractional Lie symmetries analysis, to reduce the original fractional partial differential equations into fractional ordinary differential equations, with a numerical method. By adopting the Caputo definition of derivative, the reduced fractional ordinary equations are solved by applying the implicit trapezoidal method. The numerical results confirm the applicability and the efficiency of the proposed approach.

中文翻译：

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具有非线性源项的空间分数阶对流扩散方程的数值解

摘要 本文提出了空间分数阶对流扩散方程的数值解，该方程涉及具有非线性源项的黎曼-刘维尔导数。我们提出了一种结合分数式李对称分析的程序，用数值方法将原始分数式偏微分方程化简为分数式常微分方程。采用微分的Caputo定义，应用隐式梯形法求解约简分数阶常方程。数值结果证实了所提出方法的适用性和效率。