A difference equation can well describe a lattice problem, and its dynamical property was always modeled approximately by a differential-difference equation. This paper suggests a fractal differential-difference model by taking into account the lattice’s geometry. The fractal differential-difference Burgers equation and the fractal Klein–Gordon equation are used as examples to study the solution properties by the Lie group method, and various Lie algebras of the corresponding Lie transformation group are also obtained.

中文翻译：

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分形微分方程的李群分析

差分方程可以很好地描述晶格问题，其动力学性质总是由差分方程近似建模。本文通过考虑晶格的几何形状提出了分形微分模型。以分形微分Burgers方程和分形Klein-Gordon方程为例，研究了李群方法的解性质，并得到了相应李变换群的各种李代数。