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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 309870, 9 pages
http://dx.doi.org/10.1155/2015/309870
Research Article

Local Fractional Laplace Variational Iteration Method for Solving Diffusion and Wave Equations on Cantor Sets within Local Fractional Operators

1Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
2Department of Mathematics, Faculty of Sciences, University of Istanbul, Vezneciler, 34134 Istanbul, Turkey
3Department of Mathematics and Statistics, Faculty of Science, Tshwane University of Technology, Arcadia Campus, Building 2-117, Nelson Mandela Drive, Pretoria 0001, South Africa
4Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa

Received 14 October 2014; Accepted 26 January 2015

Academic Editor: Samir B. Belhaouari

Copyright © 2015 Hassan Kamil Jassim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The local fractional Laplace variational iteration method (LFLVIM) is employed to handle the diffusion and wave equations on Cantor set. The operators are taken in the local sense. 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. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm.