{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:35:21Z","timestamp":1760232921538,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,5]],"date-time":"2022-12-05T00:00:00Z","timestamp":1670198400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia","award":["1658"],"award-info":[{"award-number":["1658"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, we study a system of Hilfer (k,\u03c8)-fractional differential equations, subject to nonlocal boundary conditions involving Hilfer (k,\u03c8)-derivatives and (k,\u03c8)-integrals. The results for the mentioned system are established by using M\u00f6nch\u2019s fixed point theorem, then the Ulam\u2013Hyers technique is used to verify the stability of the solution for the proposed system. In general, symmetry and fractional differential equations are related to each other. When a generalized Hilfer fractional derivative is modified, asymmetric results are obtained. This study concludes with an applied example illustrating the existence results obtained by M\u00f6nch\u2019s theorem.<\/jats:p>","DOI":"10.3390\/sym14122572","type":"journal-article","created":{"date-parts":[[2022,12,5]],"date-time":"2022-12-05T07:07:31Z","timestamp":1670224051000},"page":"2572","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Applicability of M\u00f6nch\u2019s Fixed Point Theorem on a System of (k, \u03c8)-Hilfer Type Fractional Differential Equations"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9401-6481","authenticated-orcid":false,"given":"Emad","family":"Fadhal","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf 31982, Al Ahsa, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2744-6320","authenticated-orcid":false,"given":"Kinda","family":"Abuasbeh","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf 31982, Al Ahsa, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7975-7545","authenticated-orcid":false,"given":"Murugesan","family":"Manigandan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore 641020, Tamilnadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6447-6361","authenticated-orcid":false,"given":"Muath","family":"Awadalla","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf 31982, Al Ahsa, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,5]]},"reference":[{"key":"ref_1","unstructured":"Kolmanovskii, V., and Myshkis, A. 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