Application of the Local Fractional Series Expansion Method and the Variational Iteration Method to the Helmholtz Equation Involving Local Fractional Derivative Operators

By Aimin Yang, Zeng-Shun Chen, Hari M. Srivastava, Xiao-jun Yang. 2013

58 citations recorded by the source corpus.

We investigate solutions of the Helmholtz equation involving local fractional derivative operators. We make use of the series expansion method and the variational iteration method, which are based upon the local fractional derivative operators. The nondifferentiable solution of the problem is obtained by using these methods.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/fb318d3b7ce66aa67f1ea345469793522c77ba69

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In Mechanics of Materials

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets (2014, methodology): “In order to illustrate the idea of the local fractional series expansion method [24-26], we consider the local fractional differential operator equation in the form:”
A Modification Fractional Homotopy Perturbation Method for Solving Helmholtz and Coupled Helmholtz Equations on Cantor Sets (2019, unknown): “The local fractional Laplace transform of φ(μ) is given by [19,20,32,33]: LT φ(μ) = Ф(μ, w) = 1 Γ(1 + δ) E −w μ φ(μ) (dμ) , (2) where the latter integral converges and w ∈ R .”