In this paper, a general framework based on fractional-order partial differential equations allows to solve image reconstruction problems. The algorithm presented in this work combines two previous notions: a fractional derivative implementation by Discrete Fourier Transform and the edge detection by topological gradient. The purpose of the paper is to extend some existing results in image denoising problem with fractional-order diffusion equations and presents new results in image inpainting. The results emphasize the importance of particular fractional-orders.