| 关于一类函数及其分数阶微积分函数的分形维数 |
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| 引用本文： | 魏毅强,李本秀.关于一类函数及其分数阶微积分函数的分形维数[J].太原理工大学学报,2010,41(3). |
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| 作者姓名： | 魏毅强 李本秀 |
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| 作者单位： | 太原理工大学,理学院,太原,030024 |
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| 摘 要： | 将经典的Weierstrass型函数中的函数项扩展为一般的李卜希兹连续周期函数,在指数参数大于等于1的情况下讨论了这类函数及其分数阶微积分函数,得出原函数及其分数阶积分函数图像的分形维数均为1,并给出其分数阶微分函数图像维数的上下界估计.同时,利用Matlab绘制出不同α值的函数图像,使结果更直观.
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| 关 键 词： | 分数阶微积分 Hausdorff维数 K-维数 Box维数 |
On the Fractal Dimensions of a Function and Its Fractional Calculus Functions |
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| WEI Yi-qiang,LI Ben-xiu.On the Fractal Dimensions of a Function and Its Fractional Calculus Functions[J].Journal of Taiyuan University of Technology,2010,41(3). |
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| Authors: | WEI Yi-qiang LI Ben-xiu |
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| Institution: | WEI Yi-qiang,LI Ben-xiu(College of Sciences,Taiyuan University of Technology,Taiyuan 030024,China) |
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| Abstract: | The function term in classical Weierstrass-type functions was extended to the general Lipschitz continuous periodic function,and such a function and its fractional calculus functions in case of the index parameter greater than or equal to 1 were discussed.The fractal dimensions of the graphs of the original function and its fractional differential function were obtained.Mean while,by using the Matlab,their graphs with different a values were drawn to make the results more intuitive. |
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| Keywords: | fractional calculus Hausdorff dimension K-dimension Box dimension |
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