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| 1 | Fractal Dimensions of Fractional Integral of Continuous Functions显示文摘In this paper,we mainly explore fractal dimensions of fractional calculus of continuous functions defined on closed intervals.Riemann–Liouville integral of a continuous function f(x) of order v(v>0) which is written as D^(-v) f(x) has been proved to still be continuous and bounded.Furthermore,upper box dimension of D^(-v) f(x) is no more than 2 and lower box dimension of D^(-v) f(x) is no less than 1.If f(x) is a Lipshciz function,D^(-v) f(x) also is a Lipshciz function.While f(x) is differentiable on [0,1],D^(-v) f(x) is differentiable on [0,1] too.With definition of upper box dimension and further calculation,we get upper bound of upper box dimension of Riemann–Liouville fractional integral of any continuous functions including fractal functions.If a continuous function f(x) satisfying H?lder condition,upper box dimension of Riemann–Liouville fractional integral of f(x) seems no more than upper box dimension of f(x).Appeal to auxiliary functions,we have proved an important conclusion that upper box dimension of Riemann–Liouville integral of a continuous function satisfying H?lder condition of order v(v>0) is strictly less than 2-v.Riemann–Liouville fractional derivative of certain continuous functions have been discussed elementary.Fractional dimensions of Weyl–Marchaud fractional derivative of certain continuous functions have been estimated. | Yong Shun LIANG Wei Yi SU | 2016 | Acta Mathematica Sinica,English Series2016，32，12： | 1 |
| 2 | 关于分数阶q-多项式生成函数的注记显示文摘文章建立了分数q-积分与分数阶q-多项式生成函数之间的关系,给出Predrag-Sladjana-Miomir多项式的拓广定义,并讨论以q-差分方程作为形式解的生成函数问题.同时得到了Predrag-Sladjana-Miomir多项式与特定q-多项式的拓广生成函数. | 蔡利平 曹健 | 2020 | 杭州师范大学学报(自然科学版)2020，19，2： | 0 |
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