{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:04:41Z","timestamp":1760148281188,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,19]],"date-time":"2023-04-19T00:00:00Z","timestamp":1681862400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we aim to present a novel n-point composite fractional formula for approximating a Riemann\u2013Liouville fractional integral operator. With the use of the definite fractional integral\u2019s definition coupled with the generalized Taylor\u2019s formula, a novel three-point central fractional formula is established for approximating a Riemann\u2013Liouville fractional integrator. Such a new formula, which emerges clearly from the symmetrical aspects of the proposed numerical approach, is then further extended to formulate an n-point composite fractional formula for approximating the same operator. Several numerical examples are introduced to validate our findings.<\/jats:p>","DOI":"10.3390\/sym15040938","type":"journal-article","created":{"date-parts":[[2023,4,20]],"date-time":"2023-04-20T03:25:11Z","timestamp":1681961111000},"page":"938","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["The n-Point Composite Fractional Formula for Approximating Riemann\u2013Liouville Integrator"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8443-8848","authenticated-orcid":false,"given":"Iqbal M.","family":"Batiha","sequence":"first","affiliation":[{"name":"Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan"},{"name":"Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman P.O. Box 346, United Arab Emirates"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3313-506X","authenticated-orcid":false,"given":"Shameseddin","family":"Alshorm","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan"}]},{"given":"Abdallah","family":"Al-Husban","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid P.O. Box 2600, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6394-1452","authenticated-orcid":false,"given":"Rania","family":"Saadeh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan"}]},{"given":"Gharib","family":"Gharib","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan"}]},{"given":"Shaher","family":"Momani","sequence":"additional","affiliation":[{"name":"Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman P.O. Box 346, United Arab Emirates"},{"name":"Department of Mathematics, The University of Jordan, Amman 11942, Jordan"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,19]]},"reference":[{"key":"ref_1","unstructured":"Aho, A.V., Hopcroft, J.E., and Ullman, J.D. (1974). 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