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Solving Helmholtz Equation with Local Fractional Derivative Operators

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Date

2019

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MDPI

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Abstract

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.

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Coupled Helmholtz Equation, Local Fractional Variational Iteration Method, Local Fractional Laplace Transform (LFLT)

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Citation

Baleanu, Dumitru; Jassim, Hassan Kamil; Al Qurashi, Maysaa, "Solving Helmholtz Equation with Local Fractional Derivative Operators", Fractal and Fractional, Vol. 3, No. 3, (September 2019).

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Fractal and Fractional

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3

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3

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