Fractional Schrödinger equation and time dependent potentials

We investigate the solutions for a time-dependent potential by considering two scenarios for the fractional Schrödinger equation. The first scenario analyzes the influence of the time-dependent potential in the absence of the kinetic term. We obtain analytical and numerical solutions for this case by considering the Caputo fractional time derivative, which extends Rabi’s model. In the second scenario, we incorporate the kinetic term in the Schrödinger equation and consider fractional spatial derivatives. For this case, we analyze the spreading of the Gaussian wave package under the action of the time and spatial fractional differential operators. •We investigate the numerical and analytical solutions for the fractional Schrödinger equation in presence of a time-dependent potential.•We study the solutions with and without kinetics terms in fractional Schrödinger equation.•We obtain an extension of Rabi’s model by considering the Caputo fractional time derivative.•In presence of kinetics terms, we study the influence of time, space and time and space (simultaneously) fractional operators in the solutions.•We show that the diffusion of a Gaussian package in presence of fractional operators is anomalous.