{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T09:02:34Z","timestamp":1762246954923,"version":"build-2065373602"},"reference-count":34,"publisher":"EDP Sciences","issue":"5","license":[{"start":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T00:00:00Z","timestamp":1762214400000},"content-version":"vor","delay-in-days":64,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2025,9,23]]},"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p>This study investigates a class of multiobjective fractional variational problems that incorporate support functions. Utilizing the concept of higher-order pseudoinvexity, we establish duality results for these problems. We present an example of a non-trivial functional that demonstrates higher-order pseudoinvexity, distinguishing it from first-order pseudoinvexity. Our theoretical analysis elucidates the relationship between the primal and dual values within the proposed model. To validate the weak duality theorem, we also provide a practical example.<\/jats:p>","DOI":"10.1051\/ro\/2025130","type":"journal-article","created":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:45:35Z","timestamp":1758825935000},"page":"3403-3421","source":"Crossref","is-referenced-by-count":0,"title":["Higher-order duality results for multiobjective fractional variational problems involving support functions and its application"],"prefix":"10.1051","volume":"59","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3273-4776","authenticated-orcid":false,"given":"Vivek","family":"Dhingra","sequence":"first","affiliation":[{"name":"Department of Computer Science and Technology, Central University of Punjab","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9441-0534","authenticated-orcid":false,"given":"Navdeep","family":"Kailey","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Thapar Institute of Engineering and Technology","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3482-8634","authenticated-orcid":false,"given":"Izhar","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Interdisciplinary Research Center for Intelligent Secure Systems, King Fahd University of Petroleum and Minerals","place":["Saudi Arabia"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sonali","family":"Sethi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Thapar Institute of Engineering and Technology","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2025,11,4]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1002\/oca.2192","volume":"37","author":"Antczak","year":"2016","journal-title":"Opt. Control App. Methods"},{"key":"R2","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/0022-247X(92)90337-D","volume":"166","author":"Bector","year":"1992","journal-title":"J. Math. Anal. App."},{"key":"R3","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/S0022-247X(03)00481-5","volume":"286","author":"Chen","year":"2003","journal-title":"J. Math. Anal. App."},{"key":"R4","doi-asserted-by":"crossref","first-page":"809","DOI":"10.2140\/pjm.1965.15.809","volume":"15","author":"Dantzig","year":"1965","journal-title":"Pac. J. Math."},{"key":"R5","doi-asserted-by":"crossref","first-page":"3147","DOI":"10.1007\/s12190-021-01657-z","volume":"68","author":"Dhingra","year":"2022","journal-title":"J. Appl. Math. Comput."},{"key":"R6","first-page":"93","volume":"2","author":"Dorn","year":"1960","journal-title":"J. Oper. Res. Soc. Jpn."},{"key":"R7","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1515\/phys-2022-0195","volume":"20","author":"Dubey","year":"2022","journal-title":"Open Phys."},{"key":"R8","first-page":"786","volume":"3","author":"Gulati","year":"2010","journal-title":"Eur. J. Pure Appl. Math."},{"key":"R9","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1006\/jmaa.1997.5330","volume":"210","author":"Gulati","year":"1997","journal-title":"J. Math. Anal. App."},{"key":"R10","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/0022-247X(64)90086-1","volume":"8","author":"Hanson","year":"1964","journal-title":"J. Math. Anal. App."},{"key":"R11","first-page":"278","volume":"2","author":"Husain","year":"2009","journal-title":"Eur. J. Pure Appl. Math."},{"key":"R12","doi-asserted-by":"crossref","first-page":"39","DOI":"10.2298\/YJOR161217019J","volume":"28","author":"Jayswal","year":"2018","journal-title":"Yugoslav J. Oper. Res."},{"key":"R13","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1007\/s12597-014-0195-0","volume":"52","author":"Jayswal","year":"2015","journal-title":"Opsearch"},{"key":"R14","doi-asserted-by":"crossref","first-page":"1850028","DOI":"10.1142\/S0217595918500288","volume":"35","author":"Jayswal","year":"2018","journal-title":"Asia-Pac. J. Oper. Res."},{"key":"R15","doi-asserted-by":"crossref","first-page":"1453","DOI":"10.1016\/j.mcm.2012.12.007","volume":"57","author":"Kailey","year":"2013","journal-title":"Math. Comput. Model."},{"key":"R16","doi-asserted-by":"crossref","first-page":"2250008","DOI":"10.1142\/S0217595922500087","volume":"40","author":"Kaur","year":"2023","journal-title":"Asia-Pac. J. Oper. Res."},{"key":"R17","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1080\/02331939308843900","volume":"28","author":"Kim","year":"1993","journal-title":"Optimization"},{"key":"R18","doi-asserted-by":"crossref","first-page":"4553","DOI":"10.1051\/ro\/2024165","volume":"58","author":"Kumar","year":"2024","journal-title":"RAIRO-Oper. Res."},{"key":"R19","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1006\/jmaa.1994.1328","volume":"186","author":"Mishra","year":"1994","journal-title":"J. Math. Anal. App."},{"key":"R20","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1016\/j.jmaa.2006.11.054","volume":"333","author":"Mishra","year":"2007","journal-title":"J. Math. Anal. App."},{"key":"R21","doi-asserted-by":"crossref","first-page":"85","DOI":"10.2298\/YJOR0901085M","volume":"19","author":"Mititelu","year":"2009","journal-title":"Yugoslav J. Oper. Res."},{"key":"R22","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/0022-247X(67)90063-7","volume":"18","author":"Mond","year":"1967","journal-title":"J. Math. Anal. App."},{"key":"R23","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/0022-247X(68)90124-8","volume":"23","author":"Mond","year":"1968","journal-title":"J. Math. Anal. App."},{"key":"R24","unstructured":"Mond B. and Weir T., Generalized concavity and duality, in Generalized Concavity in Optimization and Economics, edited by Schaible S. and Ziemba W.T.. Academic Press, New York (1981) 263\u2013279."},{"key":"R25","first-page":"3072","volume":"60","author":"Padhan","year":"2010","journal-title":"Comput. Math. App."},{"key":"R26","doi-asserted-by":"crossref","first-page":"1334","DOI":"10.1002\/mma.2685","volume":"36","author":"Padhan","year":"2013","journal-title":"Math. Methods Appl. Sci."},{"key":"R27","doi-asserted-by":"crossref","unstructured":"Padhan S.K., Behera P.K. and Mohapatra R.N., Second-order symmetric duality andvariational problems, in Mathematics and Computing, edited by Mohapatra R.N., Chowdhury D.R. and Giri D.. Springer India, New Delhi (2015) 49\u201357.","DOI":"10.1007\/978-81-322-2452-5_4"},{"key":"R28","doi-asserted-by":"crossref","first-page":"1867","DOI":"10.3934\/jimo.2023146","volume":"20","author":"Pokharna","year":"2024","journal-title":"J. Ind. Manage. Opt."},{"key":"R29","doi-asserted-by":"crossref","first-page":"121","DOI":"10.2298\/YJOR190215004P","volume":"30","author":"Prasad","year":"2020","journal-title":"Yugoslav J. Oper. Res."},{"key":"R30","doi-asserted-by":"crossref","first-page":"295","DOI":"10.2298\/YJOR180715019S","volume":"29","author":"Sachdev","year":"2019","journal-title":"Yugoslav J. Oper. Res."},{"key":"R31","doi-asserted-by":"crossref","first-page":"605","DOI":"10.2298\/FIL2102605S","volume":"35","author":"Singh","year":"2021","journal-title":"Filomat"},{"key":"R32","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1016\/0022-247X(90)90083-R","volume":"152","author":"Smart","year":"1990","journal-title":"J. Math. Anal. App."},{"key":"R33","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/S0377-2217(01)00258-2","volume":"141","author":"Suneja","year":"2002","journal-title":"Eur. J. Oper. Res."},{"key":"R34","doi-asserted-by":"crossref","first-page":"2037","DOI":"10.1051\/ro\/2022098","volume":"56","author":"Upadhyay","year":"2022","journal-title":"RAIRO-Oper. Res."}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2025130\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T08:51:42Z","timestamp":1762246302000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2025130"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9]]},"references-count":34,"journal-issue":{"issue":"5"},"alternative-id":["ro240547"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2025130","relation":{},"ISSN":["0399-0559","2804-7303"],"issn-type":[{"type":"print","value":"0399-0559"},{"type":"electronic","value":"2804-7303"}],"subject":[],"published":{"date-parts":[[2025,9]]}}}