Abstract The non-linear anomalous diffusion in anisotropic media is using in various fields, e.g. in molecular dynamics, hydrology, financial systems, porous media analysis, etc. The Lie group method is developed to study the time-fractional diffusion equation with a source term in anisotropic media. As an application, the complete Lie group classification is performed up to the equivalence transformations for all special cases of the coefficients. Some similarity reductions are obtained for implicit cases. The analytical invariant subspace method is used in order to find some exact solutions. The work is concluded by the fractional Chebyshev pseudo-spectral (FCPS) method for constructing a numerical simulation for some of the reduced equations in the symmetry analysis section.

中文翻译：

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具有源项的各向异性非线性时间分数扩散方程：通过李点对称性、解析解和数值模拟进行分类

摘要 各向异性介质中的非线性异常扩散被广泛应用于分子动力学、水文学、金融系统、多孔介质分析等领域。在各向异性介质中。作为一个应用，完整的李群分类被执行到系数的所有特殊情况的等价变换。对于隐式情况，获得了一些相似度减少。解析不变子空间方法用于找到一些精确解。该工作通过分数切比雪夫伪谱 (FCPS) 方法结束，该方法用于为对称分析部分中的一些简化方程构建数值模拟。