{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T03:41:07Z","timestamp":1776397267871,"version":"3.51.2"},"reference-count":47,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T00:00:00Z","timestamp":1764201600000},"content-version":"vor","delay-in-days":330,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>\n                    In this study, we rigorously established\n                    <jats:italic>q<\/jats:italic>\n                    \u2010Widder\u2019s formula of first and second kind by employing the\n                    <jats:italic>q<\/jats:italic>\n                    \u2010integral within a quantum calculus framework. Our approach introduces a novel formulation of the inverse\n                    <jats:italic>q<\/jats:italic>\n                    \u2010Laplace transform, enabling simplified computation without relying on conventional complex integration methods. Several illustrative problems are solved to demonstrate the effectiveness of the proposed method. The results contribute to the theoretical foundation of\n                    <jats:italic>q<\/jats:italic>\n                    \u2010calculus and have potential applications in areas such as\n                    <jats:italic>q<\/jats:italic>\n                    \u2010quantum mechanics and the analysis of\n                    <jats:italic>q<\/jats:italic>\n                    \u2010special functions.\n                  <\/jats:p>","DOI":"10.1155\/jama\/5525705","type":"journal-article","created":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T08:26:14Z","timestamp":1764231974000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quantum Extensions of Widder\u2019s Formula via\n                    <i>q<\/i>\n                    \u2010Deformed Calculus"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7624-9342","authenticated-orcid":false,"given":"S. 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