Fractional stochastic Schrödinger evolution system with complex potential and poisson jumps: Qualitative behavior and T-controllability

Abstract

Establishing the fractional stochastic Schrödinger equations (FSSEs) in Hilbert space with complex potential and Poisson jumps is the primary goal of this work. Stochastic analysis, Mönch fixed point theorem, fractional calculus, and semigroup theory all support the possibility of a moderate solution for the suggested system. We construct and prove the criteria for the mild solution’s exponential fall. The trajectory (T-) controllability for the fractional Schrödinger equation is established in the latter portion, extending the findings of Durga and Muthukumar (2023); Grecksch and Lisei (2011); Keller (2013); Wang et al. (2012). An example is given to verify the theoretical findings gained. We discuss the use of fractional Schrödinger’s equation in the Oil and Gas Industry.

Keywords

• Existence
• Exponential stability
• Poisson jump and fractional Schrödinger equation