Image denoising based on approximate solution of fractional Cauchy-Euler equation by using complex-step method

Abstract

The complex-step derivative approximation is applied to compute numerical derivatives. In this study, we propose a new formula of fractional complex-step method utilizing Jumarie definition. Based on this method, we illustrated an approximate analytic solution for the fractional Cauchy-Euler equations. Application in image denoising is imposed by introducing a new fractional mask depending on such a solution.