Abstract
The local fractional Laplace variational iteration method is used for solving the nonhomogeneous heat equations arising in the fractal heat flow. The approximate solutions are nondifferentiable functions and their plots are also given to show the accuracy and efficiency to implement the previous method.
Highlights
Fractional calculus [1,2,3,4] was used to deal with the heat conduction equation in fractal media
Fractional heat conduction equation was studied by many researchers [5,6,7,8,9,10,11,12,13,14,15,16,17]
Povstenko considered the thermoelasticity based on the fractional heat conduction equation [7]
Summary
Fractional calculus [1,2,3,4] was used to deal with the heat conduction equation in fractal media. The nonhomogeneous heat equations arising in fractal heat flow were considered by using the local fractional Fourier series method [26]. The nondifferentiable solution of one-dimensional heat equations arising in fractal transient conduction was found by the local fractional Adomian decomposition method [28]. Our aim is to investigate the nonhomogeneous heat equations arising in heat flow with local fractional derivative. We present the one-dimensional nonhomogeneous heat equations arising in heat flow with local fractional derivatives. From (3) the local fractional Fourier law of the material in fractal media [19, 23] was suggested as follows: dα dtα.
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