State Key Laboratory of Robotics, China 
; China National Nature Science Foundation 
; Liaoning province Nature Science Foundation [2015020158-301]
This paper aims to develop a convex fractional-order variation model for image multiplicative noise removal, where the regularization parameter can be adjusted adaptively according to balancing principle at each iterations to control the trade-off between the fitness and smoothness of the denoised images. In the light of the saddle-point theory, a primal-dual algorithm has been applied to solve the proposed model, and the convergence of the algorithm is guaranteed. Simulations with comparisons are carried out to demonstrate the details preserving ability and the fast property of our proposed denoising method.