Picard Successive Approximation Method for Solving Differential Equations Arising in Fractal Heat Transfer with Local Fractional Derivative-Reference-Cited by-同舟云学术

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

Published:2014 Issue: Volume:2014 Page:1-5
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Yang Ai-Min¹²^ORCID,Zhang Cheng³,Jafari Hossein⁴^ORCID,Cattani Carlo⁵,Jiao Ying⁶

Affiliation:

1. College of Science, Hebei United University, Tangshan, China

2. College of Mechanical Engineering, Yanshan University, Qinhuangdao, China

3. School of Civil Engineering and Architecture, Chongqing Jiaotong University, Chongqing 400074, China

4. Faculty of Basic Sciences, Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol 4615143358, Iran

5. Department of Mathematics, University of Salerno, Via Ponte don Melillo, Fisciano, 84084 Salerno, Italy

6. Qinggong College, Hebei United University, Tangshan 063000, China

Abstract

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.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2014/395710.pdf

Reference30 articles.

1. A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type

2. A LITERATURE SURVEY ON NUMERICAL HEAT TRANSFER

3. A technique for obtaining approximate solutions for a class of integral equations arising in radiative heat transfer