The subject of this note is the mixed Katugampola fractional integral of a bivariate function defined on a rectangular region in the Cartesian plane. This is a natural extension of the Katugampola fractional integral of a univariate function—a concept well-received in the recent literature on fractional calculus and its applications. It is shown that the mixed Katugampola fractional integral of a prescribed bivariate function preserves properties such as boundedness, continuity and bounded variation of the function. Furthermore, we estimate fractal dimension of the graph of the mixed Katugampola integral of a continuous bivariate function. Some examples for bivariate functions that are not of bounded variation but with graphs having box dimension 2 are constructed. The findings in the current note may be viewed as a sequel to our work reported in [Appl. Math. Comp., 339, 2018, pp. 220–230].

本笔记的主题是在笛卡尔平面的矩形区域上定义的二元函数的混合 Katugampola 分数积分。这是单变量函数的 Katugampola 分数积分的自然扩展——这个概念在最近关于分数阶微积分及其应用的文献中广为接受。结果表明，规定的二元函数的混合 Katugampola 分数积分保留了函数的有界性、连续性和有界变化等特性。此外，我们估计了连续二元函数的混合 Katugampola 积分图的分形维数。构造了一些不具有有界变化但具有框维数为 2 的图的双变量函数的示例。当前笔记中的发现可能被视为我们在 [Appl. 数学。Comp., 339, 2018, pp. 220–230]。