We introduce a time-fractional telegraph diffusion model to remove high level multiplicative noise while preserving critical features such as texture and edges. The model utilizes \(\alpha ^{th}\) and \(\beta ^ {th} \) order time-fractional Caputo derivatives to capture sub-diffusive and super-diffusive behaviors, enhancing noise removal in various images such as synthetic aperture radar (SAR), texture, and natural images. To accurately capture the non-local effects of the Caputo derivatives, we apply first-order and second-order discretization schemes. Extensive experiments demonstrate superior performance of the proposed model over state-of-the-art methods in terms of PSNR, SI, MAE, and MSSIM.