{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T14:25:18Z","timestamp":1762957518209,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T00:00:00Z","timestamp":1730419200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Free University of Bozen-Bolzano","award":["IN200Z","I53C22002100003"],"award-info":[{"award-number":["IN200Z","I53C22002100003"]}]},{"name":"Provincia Autonoma di Bolzano\/Alto Adige\u2014Ripartizione Innovazione, Ricerca, Universit\u00e0 e Musei","award":["IN200Z","I53C22002100003"],"award-info":[{"award-number":["IN200Z","I53C22002100003"]}]},{"name":"INdAM-GNCS","award":["IN200Z","I53C22002100003"],"award-info":[{"award-number":["IN200Z","I53C22002100003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Solving fractional-order nonlinear equations is crucial in engineering, where precision and accuracy are essential. This study introduces a novel fractional parallel technique for solving nonlinear equations. To enhance convergence, we incorporate a simple root-finding method of order 3\u03b3 + 1 as a correction term in the parallel scheme. Theoretical analysis shows that the parallel scheme achieves a convergence order of 6\u03b3 + 3. Using a dynamical system approach, we identify optimal parameter values, and the symmetry in the dynamical planes for different fractional parameters demonstrates the method\u2019s stability and consistency in handling nonlinear problems. These parameter values are applied to the parallel scheme, yielding highly consistent results. Several engineering problems are examined to assess the method\u2019s efficiency, stability, and consistency compared to existing methods.<\/jats:p>","DOI":"10.3390\/sym16111452","type":"journal-article","created":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T09:49:14Z","timestamp":1730454554000},"page":"1452","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A New High-Order Fractional Parallel Iterative Scheme for Solving Nonlinear Equations"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2980-5801","authenticated-orcid":false,"given":"Mudassir","family":"Shams","sequence":"first","affiliation":[{"name":"Faculty of Engineering, Free University of Bozen-Bolzano (BZ), 39100 Bozen-Bolzano, Italy"},{"name":"Department of Mathematics and Statistics, Riphah International University I-14, Islamabad 44000, Pakistan"}]},{"given":"Bruno","family":"Carpentieri","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, Free University of Bozen-Bolzano (BZ), 39100 Bozen-Bolzano, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,1]]},"reference":[{"key":"ref_1","first-page":"33","article-title":"Fractional Derivatives with Applications: A Review","volume":"2","author":"Shafiq","year":"2023","journal-title":"Math. 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