Images captured under insufficient light conditions often suffer from noticeable degradation of visibility, brightness and contrast. Existing methods pose limitations on enhancing low-visibility images, especially for diverse low-light conditions. In this paper, we first propose a new variational model for estimating the illumination map based on fractional-order differential. Once the illumination map is obtained, we directly inject the well-constructed illumination map into a general image restoration model, whose regularization terms can be viewed as an adaptive mapping. Since the regularization term in the restoration part can be arbitrary, one can model the regularization term by using different off-the-shelf denoisers and do not need to explicitly design various priors on the reflectance component. Because of flexibility of the model, the desired enhanced results can be solved efficiently by techniques like the plug-and-play inspired algorithm. Numerical experiments based on three public datasets demonstrate that our proposed method outperforms other competing methods, including deep learning approaches, under three commonly used metrics in terms of visual quality and image quality assessment.