Abstract
The inhomogeneous Helmholtz equation within the local fractional derivative operator conditions is investigated in this paper. The local fractional variational iteration method is applied to obtain the nondifferentiable solutions and the graphs of the illustrative examples are also shown.
Highlights
Helmholtz equation has played an important role in the partial differential equations arising in mathematical physics [1, 2]
Rafei and Ganji reported the homotopy perturbation method to report the solution to the Helmholtz equation [5]
We are faced with the problem that there must be some calculus to deal with the nondifferentiable solution for Helmholtz equation, which was structured within the local fractional derivative [24,25,26,27,28,29,30,31,32,33,34]
Summary
Helmholtz equation has played an important role in the partial differential equations arising in mathematical physics [1, 2]. We are faced with the problem that there must be some calculus to deal with the nondifferentiable solution for Helmholtz equation, which was structured within the local fractional derivative [24,25,26,27,28,29,30,31,32,33,34]. We consider the local fractional inhomogeneous Helmholtz equation in twodimensional case [31, 32]:. The local fractional inhomogeneous Helmholtz equation in three-dimensional case was suggested as follows [29, 30]:. We use the local fractional variational iteration method [30,31,32,33,34] to solve the local fractional inhomogeneous Helmholtz equation in two-dimensional case.
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