Effects of fractional order derivative on the solution of time-fractional Cahn–Hilliard equation arising in digital image inpainting

Abstract

The Cahn–Hilliard equation is a nonlinear partial differential equation which is used in digital image inpainting to restore damaged or missing parts of degraded text and high contrast images. Due to the nonlocal property of the fractional derivative, the fractional order Cahn–Hilliard equation can describe these physical processes in more flexible way. In this paper, the effects of fractional order derivative on the solutions of time-fractional Cahn–Hilliard equation are investigated using a new modification of the homotopy analysis method and a recently developed technique, namely residual power series method. The numerical and graphical illustrations depict the accuracy and reliability of the obtained results.