Open AccessFractional differentiability of the non-smooth heat curve
Author(s) -
Guo–Cheng Wu,
Shi Xiang-Chao
Publication year - 2012
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.61.190502
Subject(s) - differentiable function , fractional calculus , euclidean geometry , mathematics , mathematical analysis , pure mathematics , geometry
There are many non-smooth objects in nature, such as coastline, rock fracture, cross section, whose differentiabilities cannot be described by ordinary calculus and methods in Euclidean geometry. The local fractional derivative is one of the potential tools to investigate the non-smooth problems. This study revisits the non-smooth curves generated from the fractional integrals and Cantor-like set. From the view of the fractional differentiable functions, the differentiabilities of the non-smooth curves are derived by using a binomial expansion.