Title: Numerical analysis of some time-fractional partial differential equations for noise removal

Authors: Moulay Rchid Sidi Ammi; Ismail Jamiai

Addresses: AMNEA Group, Department of Mathematics, Faculty of Sciences and Technics Errachidia, Moulay Ismail University, B.P. 509, Errachidia, Morocco ' AMNEA Group, Department of Mathematics, Faculty of Sciences and Technics Errachidia, Moulay Ismail University, B.P. 509, Errachidia, Morocco

Abstract: In this paper, we consider the numerical resolution of two time-fractional partial differential equations for processing image denoising, which are obtained from some classical partial differential equations for processing image denoising, edge preservation and compression by replacing the first-order time derivative with a fractional derivative of order α, with 0 < α < 1. Discrete schemes of these models are introduced based on the finite differences method. Then, stability and error estimates are derived on the approximate solutions. Numerical experiments are presented to show the robustness of these new time-fractional models to obtain better results in image denoising and restoration.

Keywords: finite differences method; fractional calculus; image processing.

DOI: 10.1504/IJDSDE.2018.089104

International Journal of Dynamical Systems and Differential Equations, 2018 Vol.8 No.1/2, pp.136 - 149

Available online: 20 Nov 2017

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