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: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/395710 |
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| _version_ | 1832552253211279360 |
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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 |
| id | doaj-art-c40ee04553d04901b3873acaca0c63b5 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| 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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