{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:32:21Z","timestamp":1760059941706,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T00:00:00Z","timestamp":1753142400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This work investigates fractional stochastic Schr\u00f6dinger evolution equations in a Hilbert space, incorporating complex potential symmetry and Poisson jumps. We establish the existence of mild solutions via stochastic analysis, semigroup theory, and the M\u00f6nch fixed-point theorem. Sufficient conditions for exponential stability are derived, ensuring asymptotic decay. We further explore trajectory controllability, identifying conditions for guiding the system along prescribed paths. A numerical example is provided to validate the theoretical results.<\/jats:p>","DOI":"10.3390\/sym17081173","type":"journal-article","created":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T15:00:42Z","timestamp":1753196442000},"page":"1173","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Stochastic Schr\u00f6dinger Evolution System with Complex Potential Symmetry Using the Riemann\u2013Liouville Fractional Derivative: Qualitative Behavior and Trajectory Controllability"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6146-5544","authenticated-orcid":false,"given":"Dimplekumar","family":"Chalishajar","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Virginia Military Institute, Lexington, VA 24450, USA"}]},{"given":"Ravikumar","family":"Kasinathan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, PSG College of Arts and Science, Coimbatore 641014, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3624-5363","authenticated-orcid":false,"given":"Ramkumar","family":"Kasinathan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, PSG College of Arts and Science, Coimbatore 641014, India"}]},{"given":"Dhanalakshmi","family":"Kasinathan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Periyar University, Salem 636011, India"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-0199-2026","authenticated-orcid":false,"given":"Himanshu","family":"Thaker","sequence":"additional","affiliation":[{"name":"Engineering Institute of Technology, West Perth, WA 6005, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,22]]},"reference":[{"key":"ref_1","first-page":"3941","article-title":"Strichartz type estimates for solutions to the Schr\u00f6dinger equation","volume":"152","author":"Chen","year":"2024","journal-title":"Proc. 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