Low visibility and high-level noise are two challenges for low-light image enhancement. In this paper, by introducing fractional order differential, we propose an end-to-end conditional generative adversarial network(GAN) to solve those two problems. For the problem of low visibility, we set up a global discriminator to improve the overall reconstruction quality and restore brightness information. For the high-level noise problem, we introduce fractional order differentiation into both the generator and the discriminator. Compared with conventional end-to-end methods, fractional order can better distinguish noise and high-frequency details, thereby achieving superior noise reduction effects while maintaining details. Finally, experimental results show that the proposed model obtains superior visual effects in low-light image enhancement. By introducing fractional order differential, we anticipate that our framework will enable high quality and detailed image recovery not only in the field of low-light enhancement but also in other fields that require details.