Document Type : Research Article
Department of mathematics, Faculty of Sciences and Technologies Mohammedia, University Hassan II, Casablanca, Morocco.
LAMAI laboratory, university of Cadi Ayyad, Faculty of sciences and technology, Marrakesh, Morocco
In this work, we present a new version of the Cahn-Hilliard equation to deal with binary image inpainting. The proposed model is unique due to its memory effect ability implemented by the time fractional derivative. Also, this model has a new diffusion term that gives a topological reconnection and a well sharpness of edges and corners. We give an existence result with some numerical tests implemented by the convexity splitting to show the efficiency of the proposed model.