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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 462535, 5 pages
Research Article

Analytical Solutions of the One-Dimensional Heat Equations Arising in Fractal Transient Conduction with Local Fractional Derivative

1College of Science, Hebei United University, Tangshan 063009, China
2College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China
3Department of Mathematics, University of Salerno, Via Ponte don Melillo, Fisciano, 84084 Salerno, Italy
4Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
5International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa
6Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou, Jiangsu 221008, China

Received 26 September 2013; Accepted 17 October 2013

Academic Editor: Abdon Atangana

Copyright © 2013 Ai-Ming Yang 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.


The one-dimensional heat equations with the heat generation arising in fractal transient conduction associated with local fractional derivative operators are investigated. Analytical solutions are obtained by using the local fractional Adomian decomposition method via local fractional calculus theory. The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.