Numerical Approximations and Fractional Calculus: Extending Boole's Rule with Riemann-LiouvilleFractional Integral Inequalities

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dc.authoridBin-Mohsin or Almohsen, Bandar/0000-0002-2160-4159
dc.authoridShehzadi, Asia/0009-0005-1101-5536
dc.authoridBudak, Huseyin/0000-0001-8843-955X
dc.authoridMateen, Abdul/0009-0004-3708-0996;
dc.contributor.authorMateen, Abdul
dc.contributor.authorHaider, Wali
dc.contributor.authorShehzadi, Asia
dc.contributor.authorBudak, Huseyin
dc.contributor.authorBin-Mohsin, Bandar
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 develops integral inequalities for first-order differentiable convex functions within the framework of fractional calculus, extending Boole-type inequalities to this domain. An integral equality involving Riemann-Liouville fractional integrals is established, forming the foundation for deriving novel fractional Boole-type inequalities tailored to differentiable convex functions. The proposed framework encompasses a wide range of functional classes, including Lipschitzian functions, bounded functions, convex functions, and functions of bounded variation, thereby broadening the applicability of these inequalities to diverse mathematical settings. The research emphasizes the importance of the Riemann-Liouville fractional operator in solving problems related to non-integer-order differentiation, highlighting its pivotal role in enhancing classical inequalities. These newly established inequalities offer sharper error bounds for various numerical quadrature formulas in classical calculus, marking a significant advancement in computational mathematics. Numerical examples, computational analysis, applications to quadrature formulas and graphical illustrations substantiate the efficacy of the proposed inequalities in improving the accuracy of integral approximations, particularly within the context of fractional calculus. Future directions for this research include extending the framework to incorporate q-calculus, symmetrized q-calculus, alternative fractional operators, multiplicative calculus, and multidimensional spaces. These extensions would enable a comprehensive exploration of Boole's formula and its associated error bounds, providing deeper insights into its performance across a broader range of mathematical and computational settings.en_US
dc.description.sponsorshipKing Saud University, Riyadh, Saudi Arabiaen_US
dc.description.sponsorship[RSP2025R158]en_US
dc.description.sponsorshipThe research is supported by Researchers Supporting Project number (RSP2025R158), King Saud University, Riyadh, Saudi Arabia.en_US
dc.identifier.doi10.3390/fractalfract9010052
dc.identifier.issn2504-3110
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-85215993943en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.urihttps://doi.org/10.3390/fractalfract9010052
dc.identifier.urihttps://hdl.handle.net/20.500.12684/21569
dc.identifier.volume9en_US
dc.identifier.wosWOS:001404089000001en_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.subjectinequalities of Boole's typeen_US
dc.subjectfractional calculusen_US
dc.subjectquadrature formulasen_US
dc.subjectRiemann-Liouville fractional integralsen_US
dc.subjecterror boundsen_US
dc.subjectfunctions with convexityen_US
dc.subjectLipschitz continuityen_US
dc.subjectboundednessen_US
dc.titleNumerical Approximations and Fractional Calculus: Extending Boole's Rule with Riemann-LiouvilleFractional Integral Inequalitiesen_US
dc.typeArticleen_US

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