<p>Anisotropic diffusion is a widely used partial differential equation (PDE) based technique that effectively removes noise and preserves edges. This technique is highly dependent on the diffusion coefficient and threshold parameter. This paper uses a generalized higher-order Atangana–Baleanu derivative, and analyzes the properties in detail to control the diffusion process. Moreover, a new fractional anisotropic diffusion model based on the Mittag–Leffler function is constructed to denoise the image, in which the new diffusion coefficients have a faster convergence speed than those found in the literature. In addition, a gray level indicator is created to remove impulse noise and preserve structure details for images. Experimental results show the superiority of the proposed method over classical and existing anisotropic diffusion models when used to remove Gaussian–impulse mixed noise, multiplicative noises (Gamma noise, Rayleigh noise and Rician noise), respectively.</p>