Novel Fractional Boole's-Type Integral Inequalities via Caputo Fractional Operator and Their Implications in Numerical Analysis

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dc.authoridBudak, Huseyin/0000-0001-8843-955X
dc.authoridMateen, Abdul/0009-0004-3708-0996
dc.authoridLoredana, Ciurdariu Tirtirau/0000-0002-1234-7939;
dc.contributor.authorHaider, Wali
dc.contributor.authorMateen, Abdul
dc.contributor.authorBudak, Hueseyin
dc.contributor.authorShehzadi, Asia
dc.contributor.authorCiurdariu, Loredana
dc.date.accessioned2025-10-11T20:47:44Z
dc.date.available2025-10-11T20:47:44Z
dc.date.issued2025
dc.departmentDüzce Üniversitesien_US
dc.description.abstractThe advancement of fractional calculus, particularly through the Caputo fractional derivative, has enabled more accurate modeling of processes with memory and hereditary effects, driving significant interest in this field. Fractional calculus also extends the concept of classical derivatives and integrals to noninteger (fractional) orders. This generalization allows for more flexible and accurate modeling of complex phenomena that cannot be adequately described using integer-order derivatives. Motivated by its applications in various scientific disciplines, this paper establishes novel n-times fractional Boole's-type inequalities using the Caputo fractional derivative. For this, a fractional integral identity is first established. Using the newly derived identity, several novel Boole's-type inequalities are subsequently obtained. The proposed inequalities generalize the classical Boole's formula to the fractional domain. Further extensions are presented for bounded functions, Lipschitzian functions, and functions of bounded variation, providing sharper bounds compared to their classical counterparts. To demonstrate the precision and applicability of the obtained results, graphical illustrations and numerical examples are provided. These contributions offer valuable insights for applications in numerical analysis, optimization, and the theory of fractional integral equations.en_US
dc.identifier.doi10.3390/math13040551
dc.identifier.issn2227-7390
dc.identifier.issue4en_US
dc.identifier.scopus2-s2.0-85218965216en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.urihttps://doi.org/10.3390/math13040551
dc.identifier.urihttps://hdl.handle.net/20.500.12684/21546
dc.identifier.volume13en_US
dc.identifier.wosWOS:001431523600001en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherMdpien_US
dc.relation.ispartofMathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.snmzKA_WOS_20250911
dc.subjectCaputo fractional operatoren_US
dc.subjectconvex functionen_US
dc.subjectLipschitzian functionen_US
dc.subjectBoole's-type integral inequalitiesen_US
dc.titleNovel Fractional Boole's-Type Integral Inequalities via Caputo Fractional Operator and Their Implications in Numerical Analysisen_US
dc.typeArticleen_US

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