Solving the time-fractional Schrodinger equation by Krylov projection methods

The time-fractional Schrodinger equation is a fundamental topic in physics and its numerical solution is still an open problem. Here we start from the possibility to express its solution by means of the Mittag-Leffler function; then we analyze some approaches based on the Krylov projection methods to approximate this function; their convergence properties are discussed, together with related issues. Numerical tests are presented to confirm the strength of the approach under investigation. (C) 2014 Elsevier Inc. All rights reserved.