In this paper, we explore upper box dimension of continuous functions on $[0,1]$ and their Riemann–Liouville fractional integral. Firstly, by comparing function limits, we prove that the upper box dimension of the Riemann–Liouville fractional order integral image of a continuous function will not exceed $2-\upsilon$, the result similar to [Y. S. Liang and W. Y. Su, Fractal dimensions of fractional integral of continuous functions, Acta Math. Appl. Sin. E32 (2016) 1494–1508]. Secondly, we prove that upper box dimension of multiple algebraic sums of continuous functions does not exceed the largest box dimension among them, backing up our conclusion with an appropriate example. Finally, we draw the same conclusions for the product of multiple continuous functions.

在本文中，我们探讨了连续函数的上框维数$[0,1]$以及他们的黎曼-刘维尔分数积分。首先，通过比较函数极限，证明连续函数的黎曼-刘维尔分数阶积分像的上框维数不会超过$2-\nu$，结果类似于 [YS Liang 和 WY Su，连续函数分数积分的分形维数，Acta Math。应用。罪。 E 32（2016）1494–1508]。其次，我们证明了连续函数的多个代数和的上框维数不超过其中最大的框维数，并用适当的例子支持了我们的结论。最后，我们对多个连续函数的乘积得出相同的结论。