{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T01:30:25Z","timestamp":1775093425027,"version":"3.50.1"},"reference-count":54,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,18]],"date-time":"2022-04-18T00:00:00Z","timestamp":1650240000000},"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>Many scholars have recently become interested in establishing integral inequalities using various known fractional operators. Fractional calculus has grown in popularity as a result of its capacity to quickly solve real-world problems. First, we establish new fractional inequalities of the Hadamard\u2013Mercer, Pachpatte\u2013Mercer, and Dragomir\u2013Agarwal\u2013Mercer types containing an exponential kernel. In this regard, the inequality proved by Jensen and Mercer plays a major role in our main results. Integral inequalities involving convexity have a wide range of applications in several domains of mathematics where symmetry is important. Both convexity and symmetry are closely linked with each other; when working on one of the topics, you can apply what you have learned to the other. We consider a new identity for differentiable mappings and present its companion bound for the Dragomir\u2013Agarwal\u2013Mercer type inequality employing a convex function. Applications involving matrices are presented. Finally, we conclude our article and discuss its future scope.<\/jats:p>","DOI":"10.3390\/sym14040836","type":"journal-article","created":{"date-parts":[[2022,4,20]],"date-time":"2022-04-20T00:22:43Z","timestamp":1650414163000},"page":"836","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Hadamard\u2013Mercer, Dragomir\u2013Agarwal\u2013Mercer, and Pachpatte\u2013Mercer Type Fractional Inclusions for Convex Functions with an Exponential Kernel and Their Applications"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4524-1951","authenticated-orcid":false,"given":"Soubhagya Kumar","family":"Sahoo","sequence":"first","affiliation":[{"name":"Department of Mathematics, Institute of Technical Education and Research, Siksha O Anusandhan University, Bhubaneswar 751030, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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, Kingsville, TX 78363, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6837-8075","authenticated-orcid":false,"given":"Pshtiwan Othman","family":"Mohammed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2751-7793","authenticated-orcid":false,"given":"Bibhakar","family":"Kodamasingh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Institute of Technical Education and Research, Siksha O Anusandhan University, Bhubaneswar 751030, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7469-5402","authenticated-orcid":false,"given":"Kamsing","family":"Nonlaopon","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2908-1807","authenticated-orcid":false,"given":"Khadijah M.","family":"Abualnaja","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hilfer, R. (2000). Applications of Fractional Calculus in Physics, World Scientific.","DOI":"10.1142\/9789812817747"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Baleanu, D., G\u00fcven\u00e7, Z.B., and Machado, J.T. (2010). New Trends in Nanotechnology and Fractional Calculus Applications, Springer.","DOI":"10.1007\/978-90-481-3293-5"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"El Shaed, M. (2003, January 2\u20136). Fractional Calculus Model of Semilunar Heart Valve Vibrations. Proceedings of the ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Chicago, IL, USA.","DOI":"10.1142\/9781848161313_0008"},{"key":"ref_4","unstructured":"Magin, R.L. (2006). 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