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Solving Helmholtz Equation with Local Fractional Derivative Operators

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Department of Mathematics, Çankaya University, 06530 Ankara, Turkey
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Institute of Space Sciences, Magurele, 077125 Bucharest, Romania
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Department of Mathematics and Statistics, Faculty of Science, Tshwane University of Technology, Private Bag X680, Pretoria 0001, South Africa
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Department of Mathematics, Faculty of Education for Pure Sciences University of Thi-Qar, Nasiriyah 64001, Iraq
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Department of Mathematics, College of Science, King Saud University, P. O. BOX 2454, Ryad 11451, Saudia Arabia
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Author to whom correspondence should be addressed.
Fractal Fract 2019, 3(3), 43; https://doi.org/10.3390/fractalfract3030043
Received: 3 July 2019 / Revised: 20 July 2019 / Accepted: 23 July 2019 / Published: 1 August 2019
The paper presents a new analytical method called the local fractional Laplace variational iteration method (LFLVIM), which is a combination of the local fractional Laplace transform (LFLT) and the local fractional variational iteration method (LFVIM), for solving the two-dimensional Helmholtz and coupled Helmholtz equations with local fractional derivative operators (LFDOs). The operators are taken in the local fractional sense. Two test problems are presented to demonstrate the efficiency and the accuracy of the proposed method. The approximate solutions obtained are compared with the results obtained by the local fractional Laplace decomposition method (LFLDM). The results reveal that the LFLVIM is very effective and convenient to solve linear and nonlinear PDEs. View Full-Text
Keywords: coupled Helmholtz equation; local fractional variational iteration method; local fractional Laplace transform (LFLT) coupled Helmholtz equation; local fractional variational iteration method; local fractional Laplace transform (LFLT)
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Baleanu, D.; Jassim, H.K.; Al Qurashi, M. Solving Helmholtz Equation with Local Fractional Derivative Operators. Fractal Fract 2019, 3, 43.

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