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Local fractional Laplace homotopy analysis method for solving non-differentiable wave equations on Cantor sets

  • Shehu MaitamaEmail author
  • Weidong Zhao
Article
  • 107 Downloads

Abstract

In this paper, we introduce a semi-analytical method called the local fractional Laplace homotopy analysis method (LFLHAM) for solving wave equations with local fractional derivatives. The LFLHAM is based on the homotopy analysis method and the local fractional Laplace transform method, respectively. The proposed analytical method was a modification of the homotopy analysis method and converged rapidly within a few iterations. The nonzero convergence-control parameter was used to adjust the convergence of the series solutions. Three examples of non-differentiable wave equations were provided to demonstrate the efficiency and the high accuracy of the proposed technique. The results obtained were completely in agreement with the results in the existing methods and their qualitative and quantitative comparison of the results.

Keywords

Local fractional Laplace homotopy analysis method Local fractional wave equations Local fractional Laplace transform Homotopy analysis method Numeric and symbolic computations 

Mathematics Subject Classification

34K50 34A12 34A30 45A05 44A05 44A20 

Notes

Acknowledgements

Funding was provided by China Scholarship Council (2017GXZ025381), National Natural Science Foundation of China (11571206).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.School of MathematicsShandong UniversityJinanPeople’s Republic of China

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