{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T14:36:35Z","timestamp":1775226995090,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,25]],"date-time":"2024-12-25T00:00:00Z","timestamp":1735084800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University of Oradea, Romania","award":["RSP2024R153"],"award-info":[{"award-number":["RSP2024R153"]}]},{"name":"King Saud University, Riyadh, Saudi Arabia","award":["RSP2024R153"],"award-info":[{"award-number":["RSP2024R153"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A non-polynomial spline is a technique that utilizes information from symmetric functions to solve mathematical or physical models numerically. This paper introduces a novel non-polynomial spline construct incorporating a rational function term to develop an efficient numerical scheme for solving time-fractional differential equations. The proposed method is specifically applied to the time-fractional KdV\u2013Burgers (TFKdV) equation. and time-fractional differential equations are crucial in physics as they provide a more accurate description of various complex processes, such as anomalous diffusion and wave propagation, by capturing memory effects and non-local interactions. Using Taylor expansion and truncation error analysis, the convergence order of the numerical scheme is derived. Stability is analyzed through the Fourier stability criterion, confirming its conditional stability. The accuracy and efficiency of the rational non-polynomial spline (RNPS) method are validated by comparing numerical results from a test example with analytical and previous solutions, using norm errors. Results are presented in 2D and 3D graphical formats, accompanied by tables highlighting performance metrics. Furthermore, the influences of time and the fractional derivative are examined through graphical analysis. Overall, the RNPS method has demonstrated to be a reliable and effective approach for solving time-fractional differential equations.<\/jats:p>","DOI":"10.3390\/sym17010016","type":"journal-article","created":{"date-parts":[[2024,12,25]],"date-time":"2024-12-25T19:19:32Z","timestamp":1735154372000},"page":"16","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["High-Accuracy Solutions to the Time-Fractional KdV\u2013Burgers Equation Using Rational Non-Polynomial Splines"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1567-0264","authenticated-orcid":false,"given":"Miguel","family":"Vivas-Cortez","sequence":"first","affiliation":[{"name":"Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Av. 12 de Octubre 1076 y Roca, Quito 17-01-2184, Ecuador"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0206-3828","authenticated-orcid":false,"given":"Majeed A.","family":"Yousif","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Education, University of Zakho, Duhok 42001, Iraq"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3954-1624","authenticated-orcid":false,"given":"Bewar A.","family":"Mahmood","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Duhok, Duhok 42001, Iraq"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6837-8075","authenticated-orcid":false,"given":"Pshtiwan Othman","family":"Mohammed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7600-1729","authenticated-orcid":false,"given":"Nejmeddine","family":"Chorfi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2855-7535","authenticated-orcid":false,"given":"Alina Alb","family":"Lupas","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1080\/00207390410001686571","article-title":"A brief historical introduction to fractional calculus","volume":"35","author":"Debnath","year":"2004","journal-title":"Int. J. Math. Educ. Sci. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Tepljakov, A. (2017). Fractional-Order Modeling and Control of Dynamic Systems, Springer.","DOI":"10.1007\/978-3-319-52950-9"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Chen, W., Sun, H., and Li, X. (2022). 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