<p>Noise removal in image processing, i.e., image denoising, is a fundamental and important aspect of image processing, yet the study of effective methods continues to present a significant challenge. Traditional approaches based on anisotropic diffusion techniques often rely on integer-order derivatives, which can eliminate textures and produce staircase effects. To address these limitations, we propose a novel time-fractional anisotropic diffusion system based on the directional Laplacian for image denoising. This model offers two key advantages. First, the fractional derivative introduces additional degrees of freedom, allowing the intensity and range of diffusion to be controlled by adjusting the fractional order, enhancing the denoising effect’s flexibility and adaptability. Second, the directional Laplacian facilitates diffusion along edges, thereby better preserving the image’s edge structures. Furthermore, we establish the existence and uniqueness of the weak solution for the proposed model. To implement this model, we develop an efficient numerical scheme in this paper. The time-fractional derivative is approximated using a finite difference scheme, while the central difference scheme is employed for space discretization. We also analyze the stability and convergence of the numerical scheme. During the experimental process, we design a monotonically increasing function with respect to the image gradient values to adaptively determine the fractional order. Extensive experiments demonstrate that our model outperforms existing methods in both visualization and quality evaluation. It can effectively remove the Gaussian noise and preserve important image structure information.</p>