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A Modification Fractional Homotopy Perturbation Method for Solving Helmholtz and Coupled Helmholtz Equations on Cantor Sets

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Department of Mathematics, Faculty of Art and Sciences, Çankaya University, Ankara 06530, Turkey
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Institute of Space Sciences, Magurele-Bucharest 077125, Romania
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Department of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah 64001, Iraq
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Author to whom correspondence should be addressed.
Fractal Fract 2019, 3(2), 30; https://doi.org/10.3390/fractalfract3020030
Received: 12 May 2019 / Revised: 27 May 2019 / Accepted: 31 May 2019 / Published: 3 June 2019
In this paper, we apply a new technique, namely, the local fractional Laplace homotopy perturbation method (LFLHPM), on Helmholtz and coupled Helmholtz equations to obtain analytical approximate solutions. The iteration procedure is based on local fractional derivative operators (LFDOs). This method is a combination of the local fractional Laplace transform (LFLT) and the homotopy perturbation method (HPM). The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique. View Full-Text
Keywords: Helmholtz equation; local fractional homotopy perturbation method; local fractional Laplace transform; local fractional derivative operator Helmholtz equation; local fractional homotopy perturbation method; local fractional Laplace transform; local fractional derivative operator
MDPI and ACS Style

Baleanu, D.; Jassim, H.K. A Modification Fractional Homotopy Perturbation Method for Solving Helmholtz and Coupled Helmholtz Equations on Cantor Sets. Fractal Fract 2019, 3, 30.

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