{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T22:50:40Z","timestamp":1772491840696,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T00:00:00Z","timestamp":1750896000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Regional Development and Cohesion Funds (ERDF) 2021\u20132027","award":["AI4AM-EFRE1052"],"award-info":[{"award-number":["AI4AM-EFRE1052"]}]},{"name":"INdAM-GNCS","award":["AI4AM-EFRE1052"],"award-info":[{"award-number":["AI4AM-EFRE1052"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Fractional calculus plays a central role in modeling memory-dependent processes and complex dynamics across various fields, including control theory, fluid mechanics, and bioengineering. This study introduces an efficient and stable fractional-order iterative method based on the Caputo derivative for solving nonlinear equations. By employing a Taylor series expansion, a local convergence analysis shows that for\u00a0\u03b3\u2208(0,1], the method achieves a convergence order of\u00a02\u03b3+1. To address challenges related to memory effects and instability in existing approaches, the proposed scheme incorporates parameter optimization through chaos and bifurcation analysis. Dynamical plane analysis reveals that parameter values within chaotic regimes lead to divergence, while those in stable regions converge uniformly. The method\u2019s performance is evaluated using a set of nonlinear models drawn from biomedical engineering, including enzyme kinetics with inhibition, extended glucose\u2013insulin regulation, drug dose\u2013responses, and lung volume\u2013pressure dynamics. Comparative results demonstrate that the proposed approach outperforms existing methods in terms of iteration count, residual error, CPU time, convergence order, fractal behavior, and memory efficiency. These findings underscore the method\u2019s applicability to complex systems characterized by nonlinearity and memory effects in scientific and engineering contexts.<\/jats:p>","DOI":"10.3390\/a18070389","type":"journal-article","created":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T11:15:23Z","timestamp":1750936523000},"page":"389","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Chaos-Enhanced Fractional-Order Iterative Methods for the Stable and Efficient Solution of Nonlinear Engineering Problems"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2980-5801","authenticated-orcid":false,"given":"Mudassir","family":"Shams","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Arts and Science, Bal\u0131kesir University, Bal\u0131kesir 10145, Turkey"},{"name":"Faculty of Engineering, Free University of Bozen-Bolzano (BZ), 39100 Bolzano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bruno","family":"Carpentieri","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, Free University of Bozen-Bolzano (BZ), 39100 Bolzano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,26]]},"reference":[{"key":"ref_1","unstructured":"Noor, A.K., and Dwoyer, D.L. 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