Schrodinger equation involving fractional operators with non-singular kernel

Abstract

An alternative model of fractional Schrodinger equation involving Caputo-Fabrizio fractional operator and the new fractional operator based on the Mittag-Leffler function is proposed. We obtain the eigenvalues and eigenfunctions for a free particle moving in the infinite potential well. Numerical simulations of alternative models are presented for evaluating the effectiveness of these representations. We showed that fractional Schrodinger equation via Caputo-Fabrizio operator is a particular case of fractional Schrodinger equation obtained with the new fractional operator based in the Mittag-Leffler function.