【摘要】 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.更多还原

【Abstract】 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.更多还原