Abstract
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.
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