{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T10:07:23Z","timestamp":1774519643753,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,4]],"date-time":"2024-01-04T00:00:00Z","timestamp":1704326400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This study develops a new definition of a fractional derivative that mixes the definitions of fractional derivatives with singular and non-singular kernels. This developed definition encompasses many types of fractional derivatives, such as the Riemann\u2013Liouville and Caputo fractional derivatives for singular kernel types, as well as the Caputo\u2013Fabrizio, the Atangana\u2013Baleanu, and the generalized Hattaf fractional derivatives for non-singular kernel types. The associate fractional integral of the new mixed fractional derivative is rigorously introduced. Furthermore, a novel numerical scheme is developed to approximate the solutions of a class of fractional differential equations (FDEs) involving the mixed fractional derivative. Finally, an application in computational biology is presented.<\/jats:p>","DOI":"10.3390\/computation12010007","type":"journal-article","created":{"date-parts":[[2024,1,5]],"date-time":"2024-01-05T05:12:17Z","timestamp":1704431537000},"page":"7","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":65,"title":["A New Mixed Fractional Derivative with Applications in Computational Biology"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5032-3639","authenticated-orcid":false,"given":"Khalid","family":"Hattaf","sequence":"first","affiliation":[{"name":"Equipe de Recherche en Mod\u00e9lisation et Enseignement des Math\u00e9matiques (ERMEM), Centre R\u00e9gional des M\u00e9tiers de l\u2019Education et de la Formation (CRMEF), Derb Ghalef, Casablanca 20340, Morocco"},{"name":"Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M\u2019Sick, Hassan II University of Casablanca, Sidi Othman, Casablanca P.O. Box 7955, Morocco"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,4]]},"reference":[{"key":"ref_1","unstructured":"Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier. North-Holland Mathematics Studies."},{"key":"ref_2","unstructured":"Podlubny, I. (1999). Fractional Differential Equations, Academic Press."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1111\/j.1365-246X.1967.tb02303.x","article-title":"Linear models of dissipation whose Q is almost frequency independent-II","volume":"13","author":"Caputo","year":"1967","journal-title":"Geophys. J. Int."},{"key":"ref_4","first-page":"73","article-title":"A new definition of fractional derivative without singular kernel","volume":"1","author":"Caputo","year":"2015","journal-title":"Prog. Fract. Differ. 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