Development of Fractional Newton-Type Inequalities Through Extended Integral Operators

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dc.authoridHyder, Abd-Allah/0000-0001-9273-9512
dc.authoridBudak, Huseyin/0000-0001-8843-955X;
dc.contributor.authorHyder, Abd-Allah
dc.contributor.authorAlmoneef, Areej A.
dc.contributor.authorBarakat, Mohamed A.
dc.contributor.authorBudak, Huseyin
dc.contributor.authorAktas, Ozge
dc.date.accessioned2025-10-11T20:47:48Z
dc.date.available2025-10-11T20:47:48Z
dc.date.issued2025
dc.departmentDüzce Üniversitesien_US
dc.description.abstractThis paper introduces a new class of Newton-type inequalities (NTIs) within the framework of extended fractional integral operators. This study begins by establishing a fundamental identity for generalized fractional Riemann-Liouville (FR-L) operators, which forms the basis for deriving various inequalities under different assumptions on the integrand. In particular, fractional counterparts of the classical 1/3 and 3/8 Simpson rules are obtained when the modulus of the first derivative is convex. The analysis is further extended to include functions that satisfy a Lipschitz condition or have bounded first derivatives. Moreover, an additional NTI is presented for functions of bounded variation, expressed in terms of their total variation. In all scenarios, the proposed results reduce to classical inequalities when the fractional parameters are specified accordingly, thus offering a unified perspective on numerical integration through fractional operators.en_US
dc.description.sponsorshipKing Khalid Universityen_US
dc.description.sponsorshipPrincess Nourah bint Abdulrahman University [PNURSP2025R337]en_US
dc.description.sponsorship[RGP.2/163/46]en_US
dc.description.sponsorshipThis research was funded by King Khalid University, Grant (RGP.2/163/46) and Princess Nourah bint Abdulrahman University, Grant (PNURSP2025R337).en_US
dc.identifier.doi10.3390/fractalfract9070443
dc.identifier.issn2504-3110
dc.identifier.issue7en_US
dc.identifier.scopus2-s2.0-105011724340en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.urihttps://doi.org/10.3390/fractalfract9070443
dc.identifier.urihttps://hdl.handle.net/20.500.12684/21567
dc.identifier.volume9en_US
dc.identifier.wosWOS:001535541500001en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherMdpien_US
dc.relation.ispartofFractaland Fractionalen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.snmzKA_WOS_20250911
dc.subjectNewton-type inequalitiesen_US
dc.subjectgeneralized fractional operatorsen_US
dc.subjectwell-behaved functionsen_US
dc.titleDevelopment of Fractional Newton-Type Inequalities Through Extended Integral Operatorsen_US
dc.typeArticleen_US

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