关于一类分形函数的分数阶微积分函数及其图形的K-维数  

On fractional calculus functions with a class of fractal function and K-dimensions of their graphs

作　　者：张慧琛[1] 

机构地区：[1]忻州师范学院数学系,山西忻州034000

出　　处：《兰州理工大学学报》2011年第1期164-167,共4页Journal of Lanzhou University of Technology

摘　　要：应用Riemann-Liouville分数阶微积分的定义研究一类Weierstrass分形函数的分数阶微分函数与分数阶积分函数,给出它们的连续性,并在此基础上讨论满足一定条件时,这类Weierstrass函数的分数阶微分与积分的阶与原函数的K-维数间存在线性关系,并给予证明.On the basis of definition of Riemann-Liouville fractional calculus,fractional differential function and fractional integral function with Weierstrass function fractal were studied and their continuity was given in this paper.Under certain conditions,the linear relationship between the order of fractional differential,and integral of a Weierstrass function and the K-dimensions of primary function was proved.

关 键 词：分形 分形函数 WEIERSTRASS函数 分数阶微积分 K-维数 

分 类 号：O172.2[理学—数学]