{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T08:47:38Z","timestamp":1768294058983,"version":"3.49.0"},"reference-count":16,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T00:00:00Z","timestamp":1637625600000},"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>The main aim of this work is to study an extension of the Caputo fractional derivative operator by use of the two-parameter Mittag\u2013Leffler function given by Wiman. We have studied some generating relations, Mellin transforms and other relationships with extended hypergeometric functions in order to derive this extended operator. Due to symmetry in the family of special functions, it is easy to study their various properties with the extended fractional derivative operators.<\/jats:p>","DOI":"10.3390\/sym13122238","type":"journal-article","created":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T03:12:40Z","timestamp":1638328360000},"page":"2238","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["An Extension of Caputo Fractional Derivative Operator by Use of Wiman\u2019s Function"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0953-751X","authenticated-orcid":false,"given":"Rahul","family":"Goyal","sequence":"first","affiliation":[{"name":"Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7556-8942","authenticated-orcid":false,"given":"Praveen","family":"Agarwal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9073-3288","authenticated-orcid":false,"given":"Alexandra","family":"Parmentier","sequence":"additional","affiliation":[{"name":"National Institute of Astrophysics\u2014IAPS, 00133 Rome, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1694-7907","authenticated-orcid":false,"given":"Clemente","family":"Cesarano","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University Uninettuno, 00186 Rome, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/S0377-0427(96)00102-1","article-title":"Extension of Euler\u2019s Beta function","volume":"78","author":"Chaudhry","year":"1997","journal-title":"J. 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