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Local fractional similarity solution for the diffusion equation defined on Cantor sets
Journal article   Open access  Peer reviewed

Local fractional similarity solution for the diffusion equation defined on Cantor sets

Xiao-Jun Yang, Dumitru Baleanu and H.M. Srivastava
Applied mathematics letters, Vol.47, pp.54-60
09/2015
DOI: https://doi.org/10.1016/j.aml.2015.02.024

Abstract

Diffusion equation Local fractional derivative Local fractional partial derivative operators Non-differentiability Similarity solution
In this letter, the local fractional similarity solution is addressed for the non-differentiable diffusion equation. Structuring the similarity transformations via the rule of the local fractional partial derivative operators, we transform the diffusive operator into a similarity ordinary differential equation. The obtained result shows the non-differentiability of the solution suitable to describe the properties and behaviors of the fractal content.
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https://doi.org/10.1016/j.aml.2015.02.024View
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