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

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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.

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Funding

The work of first author was supported by Science and Engineering Research Board (SERB), DST, Govt. of India, SPG Project File No. SPG/2021/002891.

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Author notes

  1. N. Durga contributed equally to this work.

Authors and Affiliations

  1. Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai Campus, Chennai, Tamil Nadu, 600127, India

    N. Durga

  2. Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Tamil Nadu, 624302, India

    P. Muthukumar

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  1. N. Durga
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  2. P. Muthukumar
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Correspondence to P. Muthukumar.

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Durga, N., Muthukumar, P. Exponential Behaviour of Nonlinear Fractional Schrödinger Evolution Equation with Complex Potential and Poisson Jumps. J Theor Probab 36, 1939–1955 (2023). https://doi.org/10.1007/s10959-023-01266-5

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  • DOI: https://doi.org/10.1007/s10959-023-01266-5

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