{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:21:25Z","timestamp":1760235685943,"version":"build-2065373602"},"reference-count":53,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,17]],"date-time":"2021-09-17T00:00:00Z","timestamp":1631836800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007345","name":"King Mongkut's University of Technology North Bangkok","doi-asserted-by":"publisher","award":["KMUTNB-62-KNOW-26"],"award-info":[{"award-number":["KMUTNB-62-KNOW-26"]}],"id":[{"id":"10.13039\/501100007345","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we first prove three identities for functions of bounded variations. Then, by using these equalities, we obtain several trapezoid- and Ostrowski-type inequalities via generalized fractional integrals for functions of bounded variations with two variables. Moreover, we present some results for Riemann\u2013Liouville fractional integrals by special choice of the main results. Finally, we investigate the connections between our results and those in earlier works. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.<\/jats:p>","DOI":"10.3390\/sym13091724","type":"journal-article","created":{"date-parts":[[2021,9,22]],"date-time":"2021-09-22T03:47:35Z","timestamp":1632282455000},"page":"1724","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On Some New Fractional Ostrowski- and Trapezoid-Type Inequalities for Functions of Bounded Variations with Two Variables"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8455-1402","authenticated-orcid":false,"given":"Thanin","family":"Sitthiwirattham","sequence":"first","affiliation":[{"name":"Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H\u00fcseyin","family":"Budak","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Arts, D\u00fczce University, 81620 D\u00fczce, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hasan","family":"Kara","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Arts, D\u00fczce University, 81620 D\u00fczce, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5341-4926","authenticated-orcid":false,"given":"Muhammad Aamir","family":"Ali","sequence":"additional","affiliation":[{"name":"Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiraporn","family":"Reunsumrit","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1007\/BF01214290","article-title":"\u00dcber die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert","volume":"10","author":"Ostrowski","year":"1938","journal-title":"Comment. 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