Some Remarks on One-dimensional Functions and Their Riemann–Liouville Fractional Calculus  

作　　者：Qi ZHANG 

机构地区：[1]Faculty of Science,Nanjing University of Aeronautics and Astronautics

出　　处：《Acta Mathematica Sinica,English Series》2014年第3期517-524,共8页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11201230);Natural Science Foundation of Jiangsu Province(Grant No.BK2012398)

摘　　要：A one-dimensional continuous function of unbounded variation on [0, 1] has been con- structed. 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.A one-dimensional continuous function of unbounded variation on [0, 1] has been con- structed. 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.

关 键 词：Box dimension Hausdorff dimension fractional integral fractal function 

分 类 号：O172[理学—数学]