Error estimates for perturbed Milne-type inequalities by twice-differentiable functions using conformable fractional integrals

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dc.contributor.authorUnes, Esra
dc.contributor.authorDemir, Izzettin
dc.date.accessioned2025-10-11T20:48:02Z
dc.date.available2025-10-11T20:48:02Z
dc.date.issued2025
dc.departmentDüzce Üniversitesien_US
dc.description.abstractMilne's inequality provides an upper bound for the error in definite integral approximations using Milne's rule, making it a useful tool for evaluating the rule's precision. For this reason, this inequality is widely applied in engineering, physics, and applied mathematics. Additionally, conformable fractional integral operators establish a stronger relationship between classical and fractional calculus, enhancing the modeling, analysis, and resolution of complex problems. Therefore, we focus on the study of conformable fractional integral operators and Milne-type inequalities, which have significant applications in various fields. In this study, we first obtain an integral identity involving conformable fractional integral operators and twice-differentiable functions. Building on this new identity, we develop various perturbed Milne-type integral inequalities for twice-differentiable convex functions. We also validate them numerically through examples, computational analysis, and visual representations. In conclusion, it is evident that our findings significantly enhance and expand upon prior findings regarding integral inequalities. In addition to improving the scope of previous discoveries, the obtained results offer meaningful approaches and methods for tackling mathematical and scientific issues.en_US
dc.identifier.doi10.1186/s13661-025-02049-z
dc.identifier.issn1687-2770
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-105005604574en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.urihttps://doi.org/10.1186/s13661-025-02049-z
dc.identifier.urihttps://hdl.handle.net/20.500.12684/21723
dc.identifier.volume2025en_US
dc.identifier.wosWOS:001492228900001en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.ispartofBoundary Value Problemsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.snmzKA_WOS_20250911
dc.subjectMilne-type integral inequalitiesen_US
dc.subjectConvex functionsen_US
dc.subjectRiemann-Liouville fractional integralsen_US
dc.subjectConformable fractional integralsen_US
dc.titleError estimates for perturbed Milne-type inequalities by twice-differentiable functions using conformable fractional integralsen_US
dc.typeArticleen_US

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