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Abstract and Applied Analysis
Volume 2016, Article ID 2913539, 5 pages
http://dx.doi.org/10.1155/2016/2913539
Research Article

The Approximate Solutions of Three-Dimensional Diffusion and Wave Equations within Local Fractional Derivative Operator

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

Received 5 June 2016; Accepted 24 August 2016

Academic Editor: Zhenhua Guo

Copyright © 2016 Hassan Kamil Jassim. 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

We used the local fractional variational iteration transform method (LFVITM) coupled by the local fractional Laplace transform and variational iteration method to solve three-dimensional diffusion and wave equations with local fractional derivative operator. This method has Lagrange multiplier equal to minus one, which makes the calculations more easily. The obtained results show that the presented method is efficient and yields a solution in a closed form. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new method.