Caputo fractional-time of a modified Cahn-Hilliard equation for the inpainting of binary images

Document Type : Research Article


1 Department of mathematics, Faculty of Sciences and Technologies Mohammedia, University Hassan II, Casablanca, Morocco.

2 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.


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