Picard successive approximation method for solving differential equations arising in fractal heat transfer with local fractional derivative. (English) Zbl 1470.35418

Summary: 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.


35R11 Fractional partial differential equations
35A35 Theoretical approximation in context of PDEs
35Q79 PDEs in connection with classical thermodynamics and heat transfer
80A19 Diffusive and convective heat and mass transfer, heat flow
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