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

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.