10.1007/s40096-023-00509-0

A novel computational approach to the local fractional Lonngren wave equation in fractal media

  • Kang-Le Wang*1,
  1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, CN

Published in Issue 2023-01-14

How to Cite

Wang, K.-L. (2023). A novel computational approach to the local fractional Lonngren wave equation in fractal media. Mathematical Sciences, 18(3 (September 2024). https://doi.org/10.1007/s40096-023-00509-0
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Abstract

Abstract The main purpose of this paper is to investigate the local fractional Lonngren wave equation, which is a generalization of Lonngren wave equation in fractal media. Firstly, an extremely effective approach is presented to obtain the fractal travelling wave solution of the local fractional Lonngren wave equation; secondly, the characteristics of fractal travelling wave solution are illustrated by some 3D graphs; finally, the comparative results of the local fractional Lonngren wave equation and the classical Lonngren wave equation are discussed. This proposed new method is simple and efficient and provides a novel idea for the study of fractal-fractional wave models in fractal media.

Keywords

  • Fractal dimension,
  • Local fractional calculus,
  • Fractal travelling wave solution,
  • Mittag–Leffler function,
  • Lonngren wave equation

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