{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:30:11Z","timestamp":1760146211394,"version":"build-2065373602"},"reference-count":49,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2024,10,18]],"date-time":"2024-10-18T00:00:00Z","timestamp":1729209600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>This paper introduces a novel numerical technique for solving fractional stochastic differential equations with neutral delays. The method employs a stepwise collocation scheme with Jacobi poly-fractonomials to consider unknown stochastic processes. For this purpose, the delay differential equations are transformed into augmented ones without delays. This transformation makes it possible to use a collocation scheme improved with Jacobi poly-fractonomials to solve the changed equations repeatedly. At each iteration, a system of nonlinear equations is generated. Next, the convergence properties of the proposed method are rigorously analyzed. Afterward, the practical utility of the proposed numerical technique is validated through a series of test examples. These examples illustrate the method\u2019s capability to produce accurate and efficient solutions.<\/jats:p>","DOI":"10.3390\/math12203273","type":"journal-article","created":{"date-parts":[[2024,10,21]],"date-time":"2024-10-21T08:53:11Z","timestamp":1729500791000},"page":"3273","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Efficient Solutions for Stochastic Fractional Differential Equations with a Neutral Delay Using Jacobi Poly-Fractonomials"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6980-9786","authenticated-orcid":false,"given":"Afshin","family":"Babaei","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, University of Mazandaran, Babolsar P.O. Box 47416-95447, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4449-8109","authenticated-orcid":false,"given":"Sedigheh","family":"Banihashemi","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, University of Mazandaran, Babolsar P.O. Box 47416-95447, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4957-9028","authenticated-orcid":false,"given":"Behrouz","family":"Parsa Moghaddam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan P.O. Box 44169-39515, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4407-4314","authenticated-orcid":false,"given":"Arman","family":"Dabiri","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Mechatronics, Southern Illinois University, Edwardsville, IL 62026, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8262-1369","authenticated-orcid":false,"given":"Alexandra","family":"Galhano","sequence":"additional","affiliation":[{"name":"Faculdade de Ci\u00eancias Naturais, Engenharias e Tecnologias, Universidade Lus\u00f3fona do Porto, Rua Augusto Rosa 24, 4000-098 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Dobrushkin, V.A. (2017). Applied Differential Equations with Boundary Value Problems, Chapman and Hall\/CRC.","DOI":"10.1201\/9781315369785"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Nandakumaran, A., Datti, P., and George, R. 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