{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T19:17:08Z","timestamp":1785957428133,"version":"3.56.0"},"reference-count":22,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,15]],"date-time":"2024-06-15T00:00:00Z","timestamp":1718409600000},"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>The field of multiplicative analysis has recently garnered significant attention, particularly in the context of solving multiplicative differential equations (MDEs). The symmetry concept in MDEs facilitates the determination of invariant solutions and the reduction of these equations by leveraging their intrinsic symmetrical properties. This study is motivated by the need for efficient methods to address MDEs, which are critical in various applications. Our novel contribution involves leveraging the fundamental properties of orthogonal polynomials, specifically Laguerre polynomials, to derive new solutions for MDEs. We introduce the definitions of Laguerre multiplicative differential equations and multiplicative Laguerre polynomials. By applying the power series method, we construct these multiplicative Laguerre polynomials and rigorously prove their basic properties. The effectiveness of our proposed solution is validated through illustrative examples, demonstrating its practical applicability and potential for advancing the field of multiplicative analysis.<\/jats:p>","DOI":"10.3390\/sym16060748","type":"journal-article","created":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T12:48:40Z","timestamp":1718628520000},"page":"748","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["An Efficient Solution of Multiplicative Differential Equations through Laguerre Polynomials"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6313-862X","authenticated-orcid":false,"given":"Hatice Yalman","family":"Kosunalp","sequence":"first","affiliation":[{"name":"Department of Accounting and Tax, G\u00f6nen Vocational School, Band\u0131rma Onyedi Eylul University, Band\u0131rma 10200, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9272-5572","authenticated-orcid":false,"given":"Selcuk","family":"Bas","sequence":"additional","affiliation":[{"name":"Department of Accounting and Tax, Bandirma Vocational School, Band\u0131rma Onyedi Eyl\u00fcl University, Band\u0131rma 10200, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Selahattin","family":"Kosunalp","sequence":"additional","affiliation":[{"name":"Department of Computer Technologies, Gonen Vocational School, Band\u0131rma Onyedi Eyl\u00fcl University, Band\u0131rma 10200, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,15]]},"reference":[{"key":"ref_1","unstructured":"Grossman, M., and Katz, R. 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