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

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.
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.