LIE GROUP ANALYSIS OF FRACTAL DIFFERENTIAL-DIFFERENCE EQUATIONS-Reference-Cited by-同舟云学术

LIE GROUP ANALYSIS OF FRACTAL DIFFERENTIAL-DIFFERENCE EQUATIONS

Published:2021-11 Issue:07 Volume:29 Page:
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

WANG YAN¹²^ORCID,XU LI¹,WANG YU-JIN¹,LIU JIAN-GEN³

Affiliation:

1. School of Science, Tianjin, University of Commerce, Tianjin 300134, P. R. China

2. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, P. R. China

3. School of Mathematics, China University of Mining and Technology, Xuzhou Jiangsu 221116, P. R. China

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.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Geometry and Topology,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X21501978

Reference55 articles.

1. Nonlinear differential–difference equations and Fourier analysis

2. New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle

3. On two-scale dimension and its applications

4. Fractal calculus and its geometrical explanation

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