Schrödinger equation involving fractional operators with non-singular kernel

Abstract

An alternative model of fractional Schrödinger 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 Schrödinger equation via Caputo–Fabrizio operator is a particular case of fractional Schrödinger equation obtained with the new fractional operator based in the Mittag–Leffler function.

Keywords:

• Schrödinger equation
• Caputo–Fabrizio operator
• Atangana–Baleanu–Caputo operator
• Mittag–Leffler function

Acknowledgements

We would like to thank to Mayra Martínez for the interesting discussions. José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: cátedras CONACyT para jovenes investigadores 2014.

Notes

The authors declare no conflict of interest.