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

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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.

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Acknowledgements

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

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  1. School of Mathematics, Shandong University, Jinan, 250100, Shandong, People’s Republic of China

    Shehu Maitama & Weidong Zhao

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  1. Shehu Maitama
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  2. Weidong Zhao
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Correspondence to Shehu Maitama.

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Communicated by José Tenreiro Machado.

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Maitama, S., Zhao, W. Local fractional Laplace homotopy analysis method for solving non-differentiable wave equations on Cantor sets. Comp. Appl. Math. 38, 65 (2019). https://doi.org/10.1007/s40314-019-0825-5

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  • DOI: https://doi.org/10.1007/s40314-019-0825-5

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