The concept of fractional calculus goes back to the 17 th century while in recent years it is becoming a useful field of research in science and engineering and plays a very important role in several research fields such as image and signal processing. This discipline has been devoted to dealing with derivatives and integrals to an arbitrary order (real or even complex) . Among various definitions such as Caputo, Riemann–Liouville, and Grunwald-Letnikov which have been provided for fractional derivatives and integrals , the first one is more popular in particular for time variables . In image processing , fractional calculus can be applied for filtering and edge detection , giving a new approach to enhance the quality of digital images . Although there are several tools for image processing some approaches based on partial differential equations (PDEs) are more interesting for numerical analysts. Mathematical models of many natural phenomena are partial differential equations or a system of PDEs with some initial and boundary conditions . PDEs are used in image processing for denoising , filtering , inpainting , restorations , segmentation and many others . PDEs popularity is due to their advantages in theory and calculations . Several methods have been proposed for reducing noises from digital images . Among several approaches proposed to solve this problem , PDE-based methods are the most powerful . In order to preserve the image structure when removing the noise , Perona and Malik were the first who applied an isotropic diffusion expressed through a linear heat equation with an anisotropic diffusion . Then, Bai and Feng proposed an anisotropic model on the basis of the space-fractional derivatives . Recently , some PDEs based on the time- fractional derivatives have been proposed for digital image denoiseing . Using the fractional time derivative , PDEs can interpolate between the heat diffusion equation and the wave equation , which leads to a mixed behavior of diffusion and wave propagation and thus edges can be preserved in highly oscillatory region s. We have focused on a recent work proposed by Zhang et al which is a time-fractional PDE for image denoising. In this thesis at first , some necessary preliminaries from real and functional analysis as well as fractional calculus are explained . Then , we investigate solving Volterra integral equations using predictor-corrector method s. After that , we follow the recent work of Zhang et al where a time-fractional diffusion-wave equation with non-local regularization has been introduced for noise reduction . The proposed PDE is transformed into a Volterra integral equation and is solved by using the Adams-Bashforth-Moulton predictor-corrector method . The proposed model is tested over some images with Gaussian noise . In order to quantify the achieved performance , we use the Peak Signal to Noise Ratio (R) which is a criterion on the basis of the original and denoised images . At the end , we could introduce two methods for solving the proposed model in order to obtain better Rs .