Local fractional similarity solution for the diffusion equation defined on Cantor sets. (September 2015)

• Record Type: Journal Article
• Authors: Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H.M.
• Is Part Of: Applied mathematics letters. Volume 47(2015:Sep.)
• Page Start: 54
• Page End: 60
• Publication Date: 2015-09
• Subjects: Similarity solution -- Diffusion equation -- Non-differentiability -- Local fractional derivative -- Local fractional partial derivative operators; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2015.02.024
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: 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.