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

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 me...

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Main Authors: Ai-Min Yang, Cheng Zhang, Hossein Jafari, Carlo Cattani, Ying Jiao
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/395710
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author Ai-Min Yang
Cheng Zhang
Hossein Jafari
Carlo Cattani
Ying Jiao
author_facet Ai-Min Yang
Cheng Zhang
Hossein Jafari
Carlo Cattani
Ying Jiao
author_sort Ai-Min Yang
collection DOAJ
description 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.
format Article
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institution Kabale University
issn 1085-3375
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language English
publishDate 2014-01-01
publisher Wiley
record_format Article
series Abstract and Applied Analysis
spelling doaj-art-c40ee04553d04901b3873acaca0c63b52025-02-03T05:59:13ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/395710395710Picard Successive Approximation Method for Solving Differential Equations Arising in Fractal Heat Transfer with Local Fractional DerivativeAi-Min Yang0Cheng Zhang1Hossein Jafari2Carlo Cattani3Ying Jiao4College of Science, Hebei United University, Tangshan, ChinaSchool of Civil Engineering and Architecture, Chongqing Jiaotong University, Chongqing 400074, ChinaFaculty of Basic Sciences, Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol 4615143358, IranDepartment of Mathematics, University of Salerno, Via Ponte don Melillo, Fisciano, 84084 Salerno, ItalyQinggong College, Hebei United University, Tangshan 063000, ChinaThe 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.http://dx.doi.org/10.1155/2014/395710
spellingShingle Ai-Min Yang
Cheng Zhang
Hossein Jafari
Carlo Cattani
Ying Jiao
Picard Successive Approximation Method for Solving Differential Equations Arising in Fractal Heat Transfer with Local Fractional Derivative
Abstract and Applied Analysis
title Picard Successive Approximation Method for Solving Differential Equations Arising in Fractal Heat Transfer with Local Fractional Derivative
title_full Picard Successive Approximation Method for Solving Differential Equations Arising in Fractal Heat Transfer with Local Fractional Derivative
title_fullStr Picard Successive Approximation Method for Solving Differential Equations Arising in Fractal Heat Transfer with Local Fractional Derivative
title_full_unstemmed Picard Successive Approximation Method for Solving Differential Equations Arising in Fractal Heat Transfer with Local Fractional Derivative
title_short Picard Successive Approximation Method for Solving Differential Equations Arising in Fractal Heat Transfer with Local Fractional Derivative
title_sort picard successive approximation method for solving differential equations arising in fractal heat transfer with local fractional derivative
url http://dx.doi.org/10.1155/2014/395710
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