Fractal heat conduction problem solved by local fractional variation iteration method

By Xiao-jun Yang, Dumitru Băleanu. 2013

279 citations recorded by the source corpus.

This paper points out a novel local fractional variational iteration method for processing the local fractional heat conduction equation arising in fractal heat transfer.

View Paper: https://www.semanticscholar.org/paper/c7b3f7925eb22bfa9d051ac7c7b7a5019849186f

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Citations in the corpus

Application of the Local Fractional Series Expansion Method and the Variational Iteration Method to the Helmholtz Equation Involving Local Fractional Derivative Operators (2013, background): “The extremum condition of un+1 is given by [37, 41, 42] δαun+1 = 0.”
Systems of Navier-Stokes equations on Cantor sets (2013, unknown): “Based on it, the Schrödinger equation [28], the heat conduction equation [27, 29], the wave equation [27, 30], and the diffusion equation on Cantor time-space [31] were suggested based on local fractional calculus theory [27, 32, 33].”
On novel nondifferentiable exact solutions to local fractional Gardner's equation using an effective technique (2020, background): “Inserting of the above values into Equations (21) and (32), we have”
The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative (2014, methodology): “For example, the local fractional variation iteration method was used to solve the heat conduction in fractal media [26, 27].”
Local Fractional Laplace Variational Iteration Method for Solving Diffusion and Wave Equations on Cantor Sets within Local Fractional Operators (2015, methodology): “According to the rule of local fractional variational iteration method, the correction functional for (14) is constructed as follows [34–37]: u n+1 (x) = u n (x)”
Local fractional series expansion method for solving wave and diffusion equations on Cantor sets (2013, unknown): “In order to deal with local fractional ordinary and partial differential equations, there are somedeveloped technologies, for example, the local fractional variational iteration method [45, 46], the local fractional Fourier series method [47, 48], the Cantor-type cylindrical-coordinate method [49], ”