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This study introduces a new family of fractional integral operators using incomplete R\u2010function kernels, advancing the theoretical foundation of FDEs further. These operators are built on the foundation of generalized composite fractional derivatives, providing an enlarged structure that can support a greater range of solutions. The proposed framework not only generalizes existing models but also adds new analytical tools to fractional calculus. Several specific situations and corollaries are provided to demonstrate the adaptability and applicability of the developed operators.<\/jats:p>","DOI":"10.1155\/ijmm\/2307705","type":"journal-article","created":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T09:40:57Z","timestamp":1778578857000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Generalized Composite Fractional Derivatives and Integral Operators With Incomplete R\u2010Function Kernels"],"prefix":"10.1155","volume":"2026","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-6823-3909","authenticated-orcid":false,"given":"Priti","family":"Purohit","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1749-8832","authenticated-orcid":false,"given":"Ravi","family":"Gupta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8020-0541","authenticated-orcid":false,"family":"Shyamsunder","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8654-2545","authenticated-orcid":false,"given":"Biniyam","family":"Shimelis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,5,12]]},"reference":[{"key":"e_1_2_15_1_2","doi-asserted-by":"publisher","DOI":"10.3934\/math.2019.2.193"},{"key":"e_1_2_15_2_2","first-page":"11","article-title":"Comparative Implementation of Fractional Blood Alcohol Model by Numerical Approach","volume":"53","author":"Kumawat S.","year":"2024","journal-title":"Critical Reviews in Biomedical Engineering"},{"key":"e_1_2_15_3_2","doi-asserted-by":"publisher","DOI":"10.1142\/s2661335224500035"},{"key":"e_1_2_15_4_2","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/ad9ae6"},{"key":"e_1_2_15_5_2","doi-asserted-by":"publisher","DOI":"10.1142\/s2661335224500072"},{"key":"e_1_2_15_6_2","doi-asserted-by":"publisher","DOI":"10.5402\/2011\/682381"},{"key":"e_1_2_15_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40819-022-01253-0"},{"key":"e_1_2_15_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.7431"},{"key":"e_1_2_15_9_2","doi-asserted-by":"publisher","DOI":"10.53391\/mmnsa.1571609"},{"key":"e_1_2_15_10_2","doi-asserted-by":"publisher","DOI":"10.1142\/s1793524524500803"},{"key":"e_1_2_15_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.10326"},{"key":"e_1_2_15_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.csite.2025.106164"},{"key":"e_1_2_15_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.csite.2025.105946"},{"key":"e_1_2_15_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.csite.2025.106399"},{"key":"e_1_2_15_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijthermalsci.2024.109355"},{"key":"e_1_2_15_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10773-024-05654-3"},{"key":"e_1_2_15_17_2","article-title":"The Internal Blood Pressure Equation Involving Incomplete I-Functions","volume":"9","author":"Jangid K.","year":"2020","journal-title":"Information Sciences Letters"},{"key":"e_1_2_15_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40009-020-00996-y"},{"key":"e_1_2_15_19_2","doi-asserted-by":"publisher","DOI":"10.2298\/fil1607779c"},{"key":"e_1_2_15_20_2","doi-asserted-by":"publisher","DOI":"10.18514\/mmn.2018.1503"},{"key":"e_1_2_15_21_2","doi-asserted-by":"publisher","DOI":"10.1201\/9781003263517-8"},{"key":"e_1_2_15_22_2","doi-asserted-by":"publisher","DOI":"10.1080\/27690911.2023.2165280"},{"key":"e_1_2_15_23_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.9360"},{"key":"e_1_2_15_24_2","doi-asserted-by":"publisher","DOI":"10.1201\/9781420036046"},{"key":"e_1_2_15_25_2","doi-asserted-by":"publisher","DOI":"10.1080\/01966324.1989.10737258"},{"key":"e_1_2_15_26_2","first-page":"2249","article-title":"An Incomplete Category Comprised of R-Functions and Their Applications","volume":"25","author":"Gupta R.","year":"2024","journal-title":"Journal of Nonlinear and Convex Analysis"},{"key":"e_1_2_15_27_2","volume-title":"The H-function: Theory and Applications","author":"Mathai A. 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