| 闭区间[0,1]上的分形插值函数的分数阶积分 |
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| 引用本文： | 潘学哉,冯志刚,左飞. 闭区间[0,1]上的分形插值函数的分数阶积分[J]. 大学数学, 2007, 23(4): 109-112 |
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| 作者姓名： | 潘学哉 冯志刚 左飞 |
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| 作者单位： | 南京师范大学,泰州学院,数学系,江苏,泰州,225300;江苏大学,理学院,江苏,镇江,212013;盐城师范学院,数学科学学院,江苏,盐城,224001 |
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| 摘 要： | 介绍了分形插值函数和迭代函数系统以及v阶黎曼-刘准尔分数阶积分的概念及相关定理.利用这些概念及定理讨论了分形插值函数的分数阶积分在[0,1]上连续性及判定[0,1]上的分形插值函数的分数阶积分也是[0,1]上的分形插值函数,并给予了证明.
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| 关 键 词： | 分形插值函数 迭代函数系统 分数阶积分 |
| 文章编号： | 1672-1454（2007）04-0109-04 |
| 修稿时间： | 2005-11-18 |
Fractional Order Calculus of Fractal Interpolation Function on [0,1] |
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| PAN Xue-zai,FENG Zhi-gang,ZUO Fei. Fractional Order Calculus of Fractal Interpolation Function on [0,1][J]. College Mathematics, 2007, 23(4): 109-112 |
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| Authors: | PAN Xue-zai FENG Zhi-gang ZUO Fei |
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| Affiliation: | 1. Mathematics Department of Taizhou College, Nanjing Normal University, Taizhou 225300, China; 2. Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China; 3. Mathematics Department of Yancheng Normal College, Yancheng 224001, China |
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| Abstract: | The thesis introduces the concept and relative theories of fractal interpolation.Function and the Reimann-Liouville fractional integral of order v.The thesis discusses continuous property of fractal interpolation function's v order integral and judge fractal interpolation function's v order integral is fractal interpolation function on [0,1] too. |
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| Keywords: | fractal interpolation function iterated function system fractional order calculus |
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