In the evolution of fractal interpolation theory, many researchers have constructed various types of non-affine fractal functions to amplify the flexibility in approximation, the \(\alpha \) -fractal function is one among the classic example of non-affine fractal functions. In general, the fractal properties such as fractal dimension, smoothness of fractal function are much influenced by the free parameter called the vertical scaling factor. Most of the research works on the FIF have been studied with constant scaling factors which obviously provide self-similar character. Since there exists nonuniform data (or functions) showing less self-similarity, for this type of functions, variable scaling factors could be the better choice instead of constant scaling factors. This chapter discusses the fractional integral of non-affine fractal functions with variable scaling parameters. Additionally, a fractional operator developed in relation with \(\alpha \) -fractal function is presented and some analytical properties such as linearity, boundedness of the fractional operator are discussed with respect to the order of Riemann-Liouville fractional integral.