{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:54:30Z","timestamp":1760147670806,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,16]],"date-time":"2023-02-16T00:00:00Z","timestamp":1676505600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research, Imam Mohammad Ibn Saud Islamic University (IMSIU)","award":["221412044"],"award-info":[{"award-number":["221412044"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Fractional differential equations are becoming more and more indispensable for modeling real-life problems. Modeling and then analyzing these fractional differential equations assists researchers in comprehending and predicting the system they want to study. This is only conceivable when their solutions are available. However, the majority of fractional differential equations lack exact solutions, and even when they do, they cannot be assessed precisely. Therefore, in order to analyze the symmetry analysis and acquire approximate solutions, one must rely on numerical approaches. In order to solve several significant fractional differential equations numerically, this work presents an effective approach. This method\u2019s versatility and simplicity are its key benefits. To verify the RKHSM\u2019s applicability, the convergence analysis and error estimations related to it are discussed. We also provide the profiles of a variety of representative numerical solutions to the problem at hand. We validated the potential, reliability, and efficacy of the RKHSM by testing some examples.<\/jats:p>","DOI":"10.3390\/sym15020532","type":"journal-article","created":{"date-parts":[[2023,2,16]],"date-time":"2023-02-16T04:01:52Z","timestamp":1676520112000},"page":"532","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Extension of the Reproducing Kernel Hilbert Space Method\u2019s Application Range to Include Some Important Fractional Differential Equations"],"prefix":"10.3390","volume":"15","author":[{"given":"Nourhane","family":"Attia","sequence":"first","affiliation":[{"name":"Ecole Nationale Sup\u00e9rieure des Sciences de la Mer et de l\u2019Am\u00e9nagement du Littoral (ENSSMAL), Campus Universitaire de Dely Ibrahim, Bois des Cars, B.P. 19, Alger 16320, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9832-1424","authenticated-orcid":false,"given":"Ali","family":"Akg\u00fcl","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Mathematics, Lebanese American University, Beirut 1102 2801, Lebanon"},{"name":"Department of Mathematics, Art and Science Faculty, Siirt University, Siirt 56100, Turkey"},{"name":"Mathematics Research Center, Department of Mathematics, Near East University, Near East Boulevard, Nicosia 99138, Mersin 10, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rubayyi T.","family":"Alqahtani","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 12211, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,16]]},"reference":[{"key":"ref_1","unstructured":"Podlubny, I. 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Math."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/532\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:37:47Z","timestamp":1760121467000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/532"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,16]]},"references-count":20,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["sym15020532"],"URL":"https:\/\/doi.org\/10.3390\/sym15020532","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,2,16]]}}}