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

Author

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  • Ai-Min Yang
  • Cheng Zhang
  • Hossein Jafari
  • Carlo Cattani
  • Ying Jiao

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.

Suggested Citation

  • Ai-Min Yang & Cheng Zhang & Hossein Jafari & Carlo Cattani & Ying Jiao, 2014. "Picard Successive Approximation Method for Solving Differential Equations Arising in Fractal Heat Transfer with Local Fractional Derivative," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, February.
    • Handle: RePEc:hin:jnlaaa:395710
    DOI: 10.1155/2014/395710
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    Cited by:

    1. Awrejcewicz, J. & Krysko, V.A. & Sopenko, A.A. & Zhigalov, M.V. & Kirichenko, A.V. & Krysko, A.V., 2017. "Mathematical modelling of physically/geometrically non-linear micro-shells with account of coupling of temperature and deformation fields," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 635-654.

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