{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T20:00:27Z","timestamp":1767211227958,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T00:00:00Z","timestamp":1660521600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007345","name":"King Mongkut\u2019s University of Technology North Bangkok","doi-asserted-by":"publisher","award":["KMUTNB-62-KNOW-30"],"award-info":[{"award-number":["KMUTNB-62-KNOW-30"]}],"id":[{"id":"10.13039\/501100007345","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper we study single-valued and multi-valued (k,\u03c8)-Hilfer-type boundary value problems of fractional order in (1,2], subject to nonlocal boundary conditions involving (k,\u03c8)-Hilfer-type derivative and integral operators. The results for single-valued case are established by using Banach and Krasnosel\u2019ski\u012d fixed point theorems as well as Leray\u2013Schauder nonlinear alternative. In the multi-valued case, we establish an existence result for the convex valued right-hand side of the inclusion via Leray\u2013Schauder nonlinear alternative for multi-valued maps, while the second one when the right-hand side has non-convex values is obtained by applying Covitz\u2013Nadler fixed point theorem for multi-valued contractions. Numerical examples illustrating the obtained theoretical results are also presented.<\/jats:p>","DOI":"10.3390\/axioms11080403","type":"journal-article","created":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T20:58:08Z","timestamp":1660597088000},"page":"403","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["On (k,\u03c8)-Hilfer Fractional Differential Equations and Inclusions with Mixed (k,\u03c8)-Derivative and Integral Boundary Conditions"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7695-2118","authenticated-orcid":false,"given":"Sotiris K.","family":"Ntouyas","sequence":"first","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 Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]},{"given":"Cholticha","family":"Nuchpong","sequence":"additional","affiliation":[{"name":"Thai-German Pre-Engineering School, College of Industrial Technology, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]},{"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":[[2022,8,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Diethelm, K. (2010). The Analysis of Fractional Differential Equations, Springer. 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