{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T07:24:57Z","timestamp":1770103497697,"version":"3.49.0"},"reference-count":41,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,12]],"date-time":"2024-01-12T00:00:00Z","timestamp":1705017600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This study presents an algorithmically efficient approach to address the complexities associated with nonlocal variable-order operators characterized by diverse definitions. The proposed method employs integro spline quasi interpolation to approximate these operators, aiming for enhanced accuracy and computational efficiency. We conduct a thorough comparison of the outcomes obtained through this approach with other established techniques, including finite difference, IQS, and B-spline methods, documented in the applied mathematics literature for handling nonlocal variable-order derivatives and integrals. The numerical results, showcased in this paper, serve as a compelling validation of the notable advantages offered by our innovative approach. Furthermore, this study delves into the impact of selecting different variable-order values, contributing to a deeper understanding of the algorithm\u2019s behavior across a spectrum of scenarios. In summary, this research seeks to provide a practical and effective solution to the challenges associated with nonlocal variable-order operators, contributing to the applied mathematics literature.<\/jats:p>","DOI":"10.3390\/computation12010014","type":"journal-article","created":{"date-parts":[[2024,1,12]],"date-time":"2024-01-12T07:47:16Z","timestamp":1705045636000},"page":"14","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order Operators"],"prefix":"10.3390","volume":"12","author":[{"given":"Nayereh","family":"Tanha","sequence":"first","affiliation":[{"name":"Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan P.O. Box 1616, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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 1616, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1165-8815","authenticated-orcid":false,"given":"Mousa","family":"Ilie","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht P.O. 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