{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,5]],"date-time":"2025-04-05T06:45:29Z","timestamp":1743835529674,"version":"3.37.3"},"reference-count":18,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,5,2]],"date-time":"2021-05-02T00:00:00Z","timestamp":1619913600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"A remarkably large number of unified integrals involving the Mittag\u2013Leffler function have been presented. Here, with the same technique as Choi and Agarwal, we propose the establishment of two generalized integral formulas involving a multivariate generalized Mittag\u2013Leffler function, which are expressed in terms of the generalized Lauricella series due to Srivastava and Daoust. We also present some interesting special cases.<\/jats:p>","DOI":"10.3390\/axioms10020081","type":"journal-article","created":{"date-parts":[[2021,5,2]],"date-time":"2021-05-02T12:05:21Z","timestamp":1619957121000},"page":"81","source":"Crossref","is-referenced-by-count":9,"title":["Certain Unified Integrals Involving a Multivariate Mittag\u2013Leffler Function"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0906-2801","authenticated-orcid":false,"given":"Shilpi","family":"Jain","sequence":"first","affiliation":[{"name":"Department of Mathematics, Poornima College of Engineering, Jaipur 302022, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0634-2370","authenticated-orcid":false,"given":"Ravi P.","family":"Agarwal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Texas A&M University, Kingsville, TX 78363, USA"}]},{"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"},{"name":"Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6960-9338","authenticated-orcid":false,"given":"Prakash","family":"Singh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Research Scholar, Poornima University, Jaipur 302022, India"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1002\/mana.19720530114","article-title":"A note on the convergence of Kampe\u00b4 de Fe\u00b4riet\u2019s double hypergeometric series","volume":"53","author":"Srivastava","year":"1985","journal-title":"Math. 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Paris"},{"key":"ref_11","first-page":"180","article-title":"Sur la fonction de Mittag-Leffler et quelques unes de ses generalizations","volume":"77","author":"Humbert","year":"1953","journal-title":"Bull. Sci. Math. Ser. II"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"667","DOI":"10.5831\/HMJ.2013.35.4.667","article-title":"Certain unified integrals involving a product of Bessel functions of the first kind","volume":"35","author":"Choi","year":"2013","journal-title":"Honam Math. J."},{"doi-asserted-by":"crossref","unstructured":"Milovanovi\u0107, G.V., and Rassias, M.T. (2014). Analytic Number Theory, Approximation Theory, and Special Functions, Springer.","key":"ref_13","DOI":"10.1007\/978-1-4939-0258-3"},{"doi-asserted-by":"crossref","unstructured":"Gorenflo, R., Kilbas, A.A., Mainardi, F., and Rogosin, S.V. (2020). Mittag-Leffler Functions, Related Topics and Applications, Springer. [2nd ed.].","key":"ref_14","DOI":"10.1007\/978-3-662-61550-8"},{"key":"ref_15","first-page":"7","article-title":"A singular integral equation with a generalized Mittag-Leffler function in the kernel","volume":"19","author":"Prabhakar","year":"1971","journal-title":"Yokohama Math. J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1155","DOI":"10.1155\/IJMMS.2005.1155","article-title":"Solutions of Volterra-type integro-differential equations with a generalized Lauricella confluent hypergeometric function in the kernels","volume":"8","author":"Saxena","year":"2005","journal-title":"Int. J. Math. Math. Sci."},{"key":"ref_17","first-page":"287","article-title":"The asypmtotic expansion of the generalized hypergeometric function","volume":"10","author":"Wright","year":"1935","journal-title":"J. Lond. Math. Soc."},{"unstructured":"Kiryakova, V. (1994). Generalized Fractional Calculus and Applications, Wiley.","key":"ref_18"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/2\/81\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,12]],"date-time":"2024-07-12T06:13:28Z","timestamp":1720764808000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/2\/81"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,2]]},"references-count":18,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["axioms10020081"],"URL":"https:\/\/doi.org\/10.3390\/axioms10020081","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2021,5,2]]}}}