On the existence and uniqueness of the weak solution to spatial fractional nonlinear diffusion equation related to image processing

This work discusses the existence and uniqueness of the weak solution to a spatial fractional diffusion equation, which can be applied in image processing. The proposed model combines the advantages of both second- and fourth-order diffusion equations along with Gaussian filtering by employing spatial fractional derivatives and a Gaussian filter. This approach enhance edges preservation and robustness to noise. The existence and uniqueness of the weak solution for the model are proved by applying Schauder's fixed-point theorem.