It is important to preserve more detailed information in image denoising. In this paper

we extend the total variation model for image denoising is which based on gradient to a new model based on fractional derivative

and then making use of the characteristic that fractional derivative and convolution integral have the same discrete formula in certain situation

We propose a variational model based on convolution integral which can be computed easily. The numerical results show that our model can not only better improve the PSNR of image

but also preserve more detailed information.