{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:37:57Z","timestamp":1760236677783,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,14]],"date-time":"2021-12-14T00:00:00Z","timestamp":1639440000000},"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>This paper represents the processing of the two-dimensional Laplace transform with the two-dimensional Marichev\u2013Saigo\u2013Maeda integral operators and two-dimensional incomplete hypergeometric function. This article provides an entirely new perspective on the Marichev\u2013Saigo\u2013Maeda operators and incomplete functions. In addition, we have included some interesting results, such as left-sided Saigo\u2013Maeda operators and right-sided Saigo\u2013Maeda operators, making this a good direction for symmetry analysis.<\/jats:p>","DOI":"10.3390\/sym13122420","type":"journal-article","created":{"date-parts":[[2021,12,14]],"date-time":"2021-12-14T22:06:10Z","timestamp":1639519570000},"page":"2420","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Two Dimensional Laplace Transform Coupled with the Marichev-Saigo-Maeda Integral Operator and the Generalized Incomplete Hypergeometric Function"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6386-6181","authenticated-orcid":false,"given":"Yasir","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Hafr Al Batin, Hafr Al Batin 31991, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adnan","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National College of Business Administration & Economics, Lahore 54660, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Shaeel","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National College of Business Administration & Economics, Lahore 54660, Pakistan"}],"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 Mathematics, Art and Science Faculty, Siirt University, Siirt 56100, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5587616","DOI":"10.1155\/2021\/5587616","article-title":"Laplace Operator with Caputo-Type Marichev\u2013Saigo\u2013Maeda Fractional Differential Operator of Extended Mittag-Leffler Function","volume":"2021","author":"Khan","year":"2021","journal-title":"Discret. 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Math."},{"key":"ref_14","first-page":"135","article-title":"A remark on integration operators involving the Gauss hypergeometric functions","volume":"11","author":"Saigo","year":"1978","journal-title":"Math. Rep. Coll. Gen. Ed. 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