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.
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.
作者
梁永顺
张琦
姚奎
LIANG Yongshun ZHANG Qi YAO Kui(Corresponding author. Institute of Science, Nanjing University of Science and Technology, Nanjing 210014, China Faculty of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210094, China Faculty of Science, PLA University of Science and Technology, Nanjing 210093,China)
出处
《数学年刊（A辑）》
CSCD
北大核心
2017年第1期117-124,共8页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.11201230)的资助
