{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:10:10Z","timestamp":1760123410508,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,2,22]],"date-time":"2023-02-22T00:00:00Z","timestamp":1677024000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007345","name":"National Science, Research and Innovation Fund (NSRF) and King Mongkut\u2019s University of Technology North Bangkok","doi-asserted-by":"publisher","award":["KMUTNB-FF-66-11"],"award-info":[{"award-number":["KMUTNB-FF-66-11"]}],"id":[{"id":"10.13039\/501100007345","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We investigate a nonlinear, nonlocal, and fully coupled boundary value problem containing mixed (k,\u03c8^)-Hilfer fractional derivative and (k,\u03c8^)-Riemann\u2013Liouville fractional integral operators. Existence and uniqueness results for the given problem are proved with the aid of standard fixed point theorems. Examples illustrating the main results are presented. The paper concludes with some interesting findings.<\/jats:p>","DOI":"10.3390\/axioms12030229","type":"journal-article","created":{"date-parts":[[2023,2,22]],"date-time":"2023-02-22T05:01:32Z","timestamp":1677042092000},"page":"229","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On a Coupled Differential System Involving (k,\u03c8)-Hilfer Derivative and (k,\u03c8)-Riemann\u2013Liouville Integral Operators"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9609-9345","authenticated-orcid":false,"given":"Ayub","family":"Samadi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh 5315836511, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7695-2118","authenticated-orcid":false,"given":"Sotiris K.","family":"Ntouyas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5350-2977","authenticated-orcid":false,"given":"Bashir","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematices, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8185-3539","authenticated-orcid":false,"given":"Jessada","family":"Tariboon","sequence":"additional","affiliation":[{"name":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,22]]},"reference":[{"key":"ref_1","unstructured":"Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of the Fractional Differential Equations, North-Holland Mathematics Studies."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Hilfer, R. (2000). 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Comput."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ntouyas, S.K., Ahmad, B., and Tariboon, J. (2022). On (k,\u03c8^)-Hilfer fractional differential equations and inclusions with mixed (k,\u03c8^)-derivative and integral boundary conditions. Axioms, 11.","DOI":"10.3390\/axioms11080403"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"111335","DOI":"10.1016\/j.chaos.2021.111335","article-title":"On the nonlinear (k,\u03c8^)-Hilfer fractional differential equations","volume":"152","author":"Kucche","year":"2021","journal-title":"Chaos Solitons Fractals"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Samadi, A., Ntouyas, S.K., and Tariboon, J. (2022). Nonlocal coupled system for (k,\u03c6)-Hilfer fractional differential equations. Fractal Fract., 6.","DOI":"10.3390\/fractalfract6050234"},{"key":"ref_15","unstructured":"Magin, R.L. (2006). 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