Control of fractional in-time Schrodinger equations via comprehensive Caputo derivative strategies

Abstract

Drawing inspiration from our recent research on anomalous wave phenomena, we analyze the additive control of fractional (in time) Schrödinger equations with "superdiffusive" properties in time. We explore two distinct cases: one with a weak Caputo derivative and the other with a strong Caputo derivative, commonly found in the scientific literature. Demonstrating approximate controllability, we show that any properly-defined solution can be driven arbitrarily close to another within any time horizon. "Localized" control functions are explicitly constructed through suitable minimization problems involving the corresponding adjoint problems in both cases. Our study offers valuable insights into effective control strategies for these novel quantum mechanical systems.