| Some Remarks on One-dimensional Functions and Their Riemann–Liouville Fractional Calculus |
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| 基金项目： | Supported by National Natural Science Foundation of China(Grant No.11201230);Natural Science Foundation of Jiangsu Province(Grant No.BK2012398) |
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| 摘 要： | A one-dimensional continuous function of unbounded variation on 0,1] has been constructed.The length of its graph is infnite,while part of this function displays fractal features.The Box dimension of its Riemann–Liouville fractional integral has been calculated.
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| 关 键 词： | 连续函数 分数阶微积分 黎曼 一维 注记 分数次积分 盒维数 |
Some remarks on one-dimensional functions and their Riemann-Liouville fractional calculus |
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| Authors: | Qi Zhang |
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| Institution: | 1. Faculty of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210094, P. R. China
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| Abstract: | A one-dimensional continuous function of unbounded variation on 0, 1] has been constructed. The length of its graph is infinite, while part of this function displays fractal features. The Box dimension of its Riemann-Liouville fractional integral has been calculated. |
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| Keywords: | Box dimension Hausdorf dimension fractional integral fractal function |
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