The impact of time-fractional Cahn–Hilliard equation that arises during the process of digital picture reconstruction

In this article, we examine the approximate solution of fourth and sixth order time-fractional Cahn-Hilliard equation by employing Shehu Adomian decomposition method. We employed Caputo, Caputo-Fabrizio, and Atangana-Baleanu in the Caputo sense fractional differential operators. When inpainting digital photographs, this equation is utilized to repair damaged or absent portions of deteriorated text and high luminance images. The acquired results are provided in the form of series. Numerical simulations were carried out and compared with the new iterative method and q-homotopy analysis method to ensure that the current technique is accurate. The aquired results are shown both numerically and visually to ensure the applicability and validity of the proposed technique. The numerical findings are coherent with previous findings. In the current investigation, uniqueness and convergence analysis are also mentioned.