The Approximate Solutions of Helmholtz and Coupled Helmholtz Equations on Cantor Sets within Local Fractional Operator

Hassan Kamil Jassim

Department of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah, Iraq.

In this paper, we proposed local fractional Laplace decomposition method to solve the
Helmholtz and coupled Helmholtz equations on Cantor sets within local fractional
operator. The approximate solutions are obtained by using the local fractional Laplace
decomposition method, which is the coupling method of local fractional Laplace
transform and Adomian decomposition method. Illustrative examples are included to
demonstrate the high accuracy and fast convergence of this new method.

Key Words: Helmholtz equation; coupled Helmholtz equations, Local fractional operator.


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