Variable-order fractional 1-Laplacian diffusion equations for multiplicative noise removal

In this paper, we study a class of fractional $1$-Laplacian diffusion equations with variable orders, proposed as a model for multiplicative noise removal. The existence and uniqueness of the weak solution are proven. To overcome the difficulties in the approximation process,we place particular emphasis on studying the density propertiesof the variable-order fractional Sobolev spaces. Numerical experiments demonstrate that our model exhibits favorable performance across the entire image.