Exponential Behaviour of Nonlinear Fractional Schrödinger Evolution Equation with Complex Potential and Poisson Jumps

N. Durga () and P. Muthukumar ()
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N. Durga: Vellore Institute of Technology
P. Muthukumar: The Gandhigram Rural Institute (Deemed to be University)

Journal of Theoretical Probability, 2023, vol. 36, issue 4, 1939-1955

Abstract: Abstract This paper aims to investigate stochastic fractional Schrödinger evolution equations with potential and Poisson jumps in Hilbert space. The solvability of the proposed system is established by using fractional calculus, semigroup theory, Krasnoselskii’s fixed point theorems and stochastic analysis. Furthermore, sufficient conditions are formulated and proved to assure that the mild solution decays exponentially to zero in the square mean. Lastly, an application is given to demonstrate the developed theory.

Keywords: Exponential stability; Existence of mild solution; Fractional Schrödinger equations; Hilbert space; Poisson jumps; 35R11; 46E20; 47J35; 60G57; 93E15 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-023-01266-5

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