1 Hossein Jafari , 2 Hassan Kamil Jassim

1 University of Mazandaran, Faculty of Mathematical Sciences, Department of Mathematics, 2 University of Thi-Qar, Faculty of Education for Pure Sciences, Department of Mathematics

**Abstract:**

In this work, we discuss solutions of the nonlinear partial differential equations on

Cantor sets within local fractional operators. The nondifferentiable approximate

solutions are obtained by using the local fractional Laplace variational iteration method,

which is the coupling method of local fractional variational iteration method and

Laplace transform. The obtained results show the efficiency and accuracy of implements

of the present method.

**Keywords:**Nonlinear differential equation; Fractional Gas dynamics equation; Cantor set;

Yang-Laplace transform; local fractional variational iteration method.

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