Abstract
In this article, we begin with the non-homogeneous model for the non-differentiable heat flow, which is described using the local fractional vector calculus, from the first law of thermodynamics in fractal media point view. We employ the local fractional variational iteration algorithm II to solve the fractal heat equations. The obtained results show the non-differentiable behaviors of temperature fields of fractal heat flow defined on Cantor sets.
Highlights
The model for the non-differentiable heat flow involving the local fractional vector calculus was discussed in Yang[1] and Cattani et al.[2]
In section ‘‘The non-homogeneous model for the nondifferentiable heat flow,’’ we provide the basic theory of the non-differentiable heat flow
The presented method is easy, simple, efficient, and accurate to solve partial differential equations (PDEs) by employing the local fractional derivatives
Summary
The model for the non-differentiable heat flow involving the local fractional vector calculus was discussed in Yang[1] and Cattani et al.[2]. Variational iteration algorithm II within local fractional derivative operator (local fractional variational iteration algorithm II (LFVIA-II)) (see Yang and Zhang[15] Liu et al.,[16] Baleanu et al.17) will be applied to deal with the non-differentiable problem in fractal heat transfer. The non-homogeneous model for the nondifferentiable heat flow We will derive the non-homogeneous models for non-differentiable heat flow.
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