In this paper, we study Riemann Liouville fractional integral of hidden variable fractal interpolation function (HVFIF) constructed by functions whose Lipschitz exponents are in (0, 1]. Firstly, we present a construction of HVFIF using functions of which Lipschitz exponents are in (0, 1], so that the Riemann Liouville fractional integral of the HVFIF becomes a fractal interpolation function, and give an example where Lipschitz exponents of functions of IFS are in (0, 1]. Secondly, we prove that the Riemann Liouville fractional integral is also a HVFIF with function vertical scaling factors defined newly. Finally, we give the graphs of 0.8- and 0.2-order fractional integrals of the HVFIFs constructed in the above example.

本文研究了由Lipschitz指数位于（0，1]的函数构造的隐变量分形插值函数（HVFIF）的Riemann Liouville分数积分。首先，我们提出了使用Lipschitz指数位于（（ 0，1]，因此HVFIF的Riemann Liouville分式积分成为分形插值函数，并以IFS函数的Lipschitz指数在（0，1]中为例。其次，我们证明Riemann Liouville分式积分也是一个新定义了函数垂直比例因子的HVFIF，最后给出了上例中构造的HVFIF的0.8阶和0.2阶分数积分的图。