The majority of methods based on fractional order differentiation for image enhancement always try to select different fractional orders and they fix the optimal one all the pixels in one image. However

these methods have difficulties in robustly enhancing images in complex environments. Therefore

a multi-bilateral filtering algorithm based on adaptive fractional order differentiation is proposed. The amplitude-frequency nonlinear joint model is established to adaptively select fractional order by analyzing the texture's characters

which can effectively overcome texture changes in images with complex environment. In the framework of bilateral filtering

introducing the guided image by adaptively selecting fractional order and detail transfer method makes sure that the texture details of an image are maintained/enhanced during denoising. Experiment results show that the proposed algorithm has better performance in computer vision and graphics

such as image filtering

dehazing and detail enhancement.