| 梁永顺,张琦,姚奎.分形插值函数的分数阶微积分的分形维数[J].数学年刊A辑,2017,38(1):0117~124 |
| 分形插值函数的分数阶微积分的分形维数 |
| Fractal Dimension of Fractional Calculus of Certain Interpolation Functions |
| Received:September 04, 2013 Revised:June 07, 2016 |
| DOI：10.16205/j.cnki.cama.2017.0010 |
| 中文关键词: Fractal dimension, Riemann-Liouville fractional calculus, Linear fractal interpolation function |
| 英文关键词:Fractal dimension, Riemann-Liouville fractional calculus, Linear fractal interpolation function |
| 基金项目:本文受到国家自然科学基金(No.11201230)的资助. |
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| 中文摘要: |
| 证明了线性分形插值函数的Riemann-Liouville分数阶微积分仍然是线性
分形插值函数. 在基于线性分形插值函数有关讨论的基础上, 证明了线性分形插值函数的Box维数与Riemann-Liouville分数阶微积分
的阶之间成立着线性关系. 文中给出的例子的图像和数值结果更进一步说明了这个结论. |
| 英文摘要: |
| Riemann-Liouville fractional calculus of a linear
fractal interpolation function (LFIF for short) is proved to be still an LFIF.
Based on the investigations dealing with the LFIF, box dimension of
Riemann-Liouville fractional calculus of such functions is shown
to be linear with respect to the order of Riemann-Liouville
fractional calculus. Graphs and numerical results of certain example
further certificate the conclusion. |
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