In this paper, we mainly study the symmetry analysis and conservation laws of the time fractional Clannish Random Walker’s Parabolic (CRWP) equation. The vector fields and similarity reduction of the time fractional CRWP equation are obtained. In addition, based on the power series theory, a simple and effective approach for constructing explicit power series solutions is proposed. Finally, by use of the new conservation theorem, the conservation laws of the time fractional CRWP equation are constructed.

中文翻译：

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时间分数 Clannish Random Walker 抛物线方程的李对称分析、显式解和守恒定律

本文主要研究时间分数Clannish Random Walker's Parabolic (CRWP)方程的对称性分析和守恒定律。得到了时间分数CRWP方程的向量场和相似性约简。此外，基于幂级数理论，提出了一种简单有效的构造显式幂级数解的方法。最后，利用新的守恒定理，构造了时间分数CRWP方程的守恒定律。