{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T07:22:24Z","timestamp":1763018544142,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,3]],"date-time":"2023-01-03T00:00:00Z","timestamp":1672704000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Recently, a new fractional derivative operator has been introduced so that it presents the combination of the Riemann\u2013Liouville integral and Caputo derivative. This paper aims to enhance the reproducing kernel Hilbert space method (RKHSM, for short) for solving certain fractional differential equations involving this new derivative. This is the first time that the application of the RKHSM is employed for solving some differential equations with the new operator. We illustrate the convergence analysis of the applicability and reliability of the suggested approaches. The results confirm that the RKHSM finds the true solution. Additionally, these numerical results indicate the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/sym15010144","type":"journal-article","created":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T01:42:44Z","timestamp":1672796564000},"page":"144","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["An Efficient Approach for Solving Differential Equations in the Frame of a New Fractional Derivative Operator"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9937-8665","authenticated-orcid":false,"given":"Nourhane","family":"Attia","sequence":"first","affiliation":[{"name":"Ecole Nationale Sup\u00e9rieure des Sciences de la Mer et de l\u2019Am\u00e9nagement du Littoral, 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":"Art and Science Faculty, Department of Mathematics, Siirt University, Siirt 56100, Turkey"},{"name":"Mathematics Research Center, Department of Mathematics, Near East University, Near East Boulevard, Nicosia 99138, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7910-3074","authenticated-orcid":false,"given":"Djamila","family":"Seba","sequence":"additional","affiliation":[{"name":"Dynamic of Engines and Vibroacoustic Laboratory, Faculty of Engineer\u2019s Sciences, University M\u2019hamed Bougara of Boumerdes, Boumerdes 35000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9103-3702","authenticated-orcid":false,"given":"Abdelkader","family":"Nour","sequence":"additional","affiliation":[{"name":"Dynamic of Engines and Vibroacoustic Laboratory, Faculty of Engineer\u2019s Sciences, University M\u2019hamed Bougara of Boumerdes, Boumerdes 35000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9320-9433","authenticated-orcid":false,"given":"Manuel De","family":"la Sen","sequence":"additional","affiliation":[{"name":"Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, 48940 Leioa, Bizkaia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2994-7201","authenticated-orcid":false,"given":"Mustafa","family":"Bayram","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Biruni University, Topkap\u0131, Istanbul 34010, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"19562","DOI":"10.3934\/math.20221074","article-title":"Analytical solution of time-fractional Schr\u00f6dinger equations via Shehu Adomian Decomposition Method","volume":"7","author":"Kapoor","year":"2022","journal-title":"AIMS Math."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ozkan, E.M. 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