{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T03:53:24Z","timestamp":1773978804172,"version":"3.50.1"},"reference-count":58,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,7]],"date-time":"2025-02-07T00:00:00Z","timestamp":1738886400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Nabil Mlaiki","award":["The author Nabil Mlaiki would like to thank Prince Sultan University for paying the APC and for the support through the TAS research lab."],"award-info":[{"award-number":["The author Nabil Mlaiki would like to thank Prince Sultan University for paying the APC and for the support through the TAS research lab."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The aim of this research article is to use the extended fractional operators involving the multivariate Mittag\u2013Leffler (M-M-L) function, we provide the generalization of the Hermite\u2013Hadamard\u2013Fejer (H-H-F) inequalities. We relate these inequalities to previously published disparities in the literature by making appropriate substitutions. In the last section, we analyze several inequalities related to the H-H-F inequalities, focusing on generalized h-convexity associated with extended fractional operators involving the M-M-L function. To achieve this, we derive two identities for locally differentiable functions, which allows us to provide specific estimates for the differences between the left, middle, and right terms in the H-H-F inequalities. Also, we have constructed specific inequalities and visualized them through graphical representations to facilitate their applications in analysis. The research bridges theoretical advancements with practical applications, providing high-accuracy bounds for complex systems involving fractional calculus.<\/jats:p>","DOI":"10.3390\/computation13020046","type":"journal-article","created":{"date-parts":[[2025,2,7]],"date-time":"2025-02-07T10:07:56Z","timestamp":1738922876000},"page":"46","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Computational Representation of Fractional Inequalities Through 2D and 3D Graphs with Applications"],"prefix":"10.3390","volume":"13","author":[{"given":"Muhammad","family":"Younis","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahsan","family":"Mehmood","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8480-2817","authenticated-orcid":false,"given":"Muhammad","family":"Samraiz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Sargodha, Sargodha P.O. Box 40100, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2728-7537","authenticated-orcid":false,"given":"Gauhar","family":"Rahman","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Statistics, Hazara University, Mansehra 21300, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Salma","family":"Haque","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9578-2073","authenticated-orcid":false,"given":"Ahmad","family":"Aloqaily","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7986-886X","authenticated-orcid":false,"given":"Nabil","family":"Mlaiki","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,7]]},"reference":[{"key":"ref_1","unstructured":"Abel, N. 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