{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:24:36Z","timestamp":1760059476685,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T00:00:00Z","timestamp":1750291200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science, Research and Innovation Fund (NSRF)","award":["KMUTNB-FF-68-B-04"],"award-info":[{"award-number":["KMUTNB-FF-68-B-04"]}]},{"DOI":"10.13039\/501100007345","name":"King Mongkut\u2019s University of Technology North Bangkok","doi-asserted-by":"publisher","award":["KMUTNB-FF-68-B-04"],"award-info":[{"award-number":["KMUTNB-FF-68-B-04"]}],"id":[{"id":"10.13039\/501100007345","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The two-parameter (p,q)-operators are a new family of operators in calculus that have shown their capabilities in modeling various systems in recent years. Following this path, in this paper, we present a new construction of the Langevin equation using two-parameter (p,q)-Caputo derivatives. For this new Langevin equation, equivalently, we obtain the solution structure as a post-quantum integral equation and then conduct an existence analysis via a fixed-point-based approach. The use of theorems such as the Krasnoselskii and Leray\u2013Schauder fixed-point theorems will guarantee the existence of solutions to this equation, whose uniqueness is later proven by Banach\u2019s contraction principle. Finally, we provide three examples in different structures and validate the results numerically.<\/jats:p>","DOI":"10.3390\/axioms14060474","type":"journal-article","created":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T08:43:58Z","timestamp":1750322638000},"page":"474","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Existence of (p,q)-Solutions for the Post-Quantum Langevin Equation: A Fixed-Point-Based Approach"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2230-2750","authenticated-orcid":false,"given":"Mohammed Jasim","family":"Mohammed","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, University of Anbar, Ramadi 31001, Iraq"}]},{"given":"Ali","family":"Ghafarpanah","sequence":"additional","affiliation":[{"name":"Department of Sciences, Salman Farsi University, Kazerun P.O. Box 73175-457, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1574-1800","authenticated-orcid":false,"given":"Sina","family":"Etemad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz P.O. Box 53714-161, Iran"},{"name":"Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Nasiriyah 64001, Iraq"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7695-2118","authenticated-orcid":false,"given":"Sotiris K.","family":"Ntouyas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8185-3539","authenticated-orcid":false,"given":"Jessada","family":"Tariboon","sequence":"additional","affiliation":[{"name":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,19]]},"reference":[{"key":"ref_1","unstructured":"Podlubny, I. (1999). 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