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Abstract and Applied Analysis
Volume 2014, Article ID 395710, 5 pages
Research Article

Picard Successive Approximation Method for Solving Differential Equations Arising in Fractal Heat Transfer with Local Fractional Derivative

1College of Science, Hebei United University, Tangshan, China
2College of Mechanical Engineering, Yanshan University, Qinhuangdao, China
3School of Civil Engineering and Architecture, Chongqing Jiaotong University, Chongqing 400074, China
4Faculty of Basic Sciences, Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol 4615143358, Iran
5Department of Mathematics, University of Salerno, Via Ponte don Melillo, Fisciano, 84084 Salerno, Italy
6Qinggong College, Hebei United University, Tangshan 063000, China

Received 12 December 2013; Accepted 1 January 2014; Published 11 February 2014

Academic Editor: Ming Li

Copyright © 2014 Ai-Min 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 Fourier law of one-dimensional heat conduction equation in fractal media is investigated in this paper. An approximate solution to one-dimensional local fractional Volterra integral equation of the second kind, which is derived from the transformation of Fourier flux equation in discontinuous media, is considered. The Picard successive approximation method is applied to solve the temperature field based on the given Mittag-Leffler-type Fourier flux distribution in fractal media. The nondifferential approximate solutions are given to show the efficiency of the present method.