| 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 |
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| 引用本文： | 张慧琛.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[J].兰州理工大学学报,2011,37(1):164-167. |
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| 作者姓名： | 张慧琛 |
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| 作者单位： | 忻州师范学院数学系,山西,忻州,034000 |
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| 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,并在此墓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.
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| 关 键 词： | 分形 分形函数 Weierstrass函数 分数阶微积分 K-维数 |
On fractional calculus functions with a class of fractal function and K-dimensions of their graphs |
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| ZHANG Hui-Chen.On fractional calculus functions with a class of fractal function and K-dimensions of their graphs[J].Journal of Lanzhou University of Technology,2011,37(1):164-167. |
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| Authors: | ZHANG Hui-Chen |
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| Institution: | ZHANG Hui-Chen(Department of Mathematics,Xinzhou Teachers' University,Shanxi 034000,China) |
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| Abstract: | 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. |
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| Keywords: | fractal fractal function Weierstrass function fractional calculus K-dimension |
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