%0 Journal Article
%T 分形插值函数的分数阶微积分的分形维数<br>Fractal Dimension of Fractional Calculus of Certain Interpolation Functions
%A 梁永顺
%A 张琦
%A 姚奎
%J 数学年刊（A辑）
%D 2017
%R 10.16205/j.cnki.cama.2017.0010
%X 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.<br>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.
%K Fractal dimension
%K Riemann-Liouville fractional calculus
%K Linear fractal interpolation function&lt
%K br&gt
%K Fractal dimension
%K Riemann-Liouville fractional calculus
%K Linear fractal interpolation function
%U http://www.camath.fudan.edu.cn/camacn/ch/reader/view_abstract.aspx?file_no=38A110&flag=1