Generalized Fractional Integral Inequalities Derived from Convexity Properties of Twice-Differentiable Functions
This study presents novel formulations of fractional integral inequalities, formulated using generalized fractional integral operators and the exploration of convexity properties. A key identity is established for twice-differentiable functions with the absolute value of their second derivative bein...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/2/97 |
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| author | Areej A. Almoneef Abd-Allah Hyder Fatih Hezenci Hüseyin Budak |
| author_facet | Areej A. Almoneef Abd-Allah Hyder Fatih Hezenci Hüseyin Budak |
| author_sort | Areej A. Almoneef |
| collection | DOAJ |
| description | This study presents novel formulations of fractional integral inequalities, formulated using generalized fractional integral operators and the exploration of convexity properties. A key identity is established for twice-differentiable functions with the absolute value of their second derivative being convex. Using this identity, several generalized fractional Hermite–Hadamard-type inequalities are developed. These inequalities extend the classical midpoint and trapezoidal-type inequalities, while offering new perspectives through convexity properties. Also, some special cases align with known results, and an illustrative example, accompanied by a graphical representation, is provided to demonstrate the practical relevance of the results. Moreover, the findings may offer potential applications in numerical integration, optimization, and fractional differential equations, illustrating their relevance to various areas of mathematical analysis. |
| format | Article |
| id | doaj-art-b9398b9703544ab3b58df110df008cdb |
| institution | DOAJ |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-b9398b9703544ab3b58df110df008cdb2025-08-20T02:44:56ZengMDPI AGFractal and Fractional2504-31102025-02-01929710.3390/fractalfract9020097Generalized Fractional Integral Inequalities Derived from Convexity Properties of Twice-Differentiable FunctionsAreej A. Almoneef0Abd-Allah Hyder1Fatih Hezenci2Hüseyin Budak3Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi ArabiaDepartment of Mathematics, Faculty of Science and Arts, Duzce University, Duzce 81620, TürkiyeDepartment of Mathematics, Faculty of Science and Arts, Duzce University, Duzce 81620, TürkiyeThis study presents novel formulations of fractional integral inequalities, formulated using generalized fractional integral operators and the exploration of convexity properties. A key identity is established for twice-differentiable functions with the absolute value of their second derivative being convex. Using this identity, several generalized fractional Hermite–Hadamard-type inequalities are developed. These inequalities extend the classical midpoint and trapezoidal-type inequalities, while offering new perspectives through convexity properties. Also, some special cases align with known results, and an illustrative example, accompanied by a graphical representation, is provided to demonstrate the practical relevance of the results. Moreover, the findings may offer potential applications in numerical integration, optimization, and fractional differential equations, illustrating their relevance to various areas of mathematical analysis.https://www.mdpi.com/2504-3110/9/2/97generalized fractional operatorsHermite–Hadamard inequalityconvex functions |
| spellingShingle | Areej A. Almoneef Abd-Allah Hyder Fatih Hezenci Hüseyin Budak Generalized Fractional Integral Inequalities Derived from Convexity Properties of Twice-Differentiable Functions Fractal and Fractional generalized fractional operators Hermite–Hadamard inequality convex functions |
| title | Generalized Fractional Integral Inequalities Derived from Convexity Properties of Twice-Differentiable Functions |
| title_full | Generalized Fractional Integral Inequalities Derived from Convexity Properties of Twice-Differentiable Functions |
| title_fullStr | Generalized Fractional Integral Inequalities Derived from Convexity Properties of Twice-Differentiable Functions |
| title_full_unstemmed | Generalized Fractional Integral Inequalities Derived from Convexity Properties of Twice-Differentiable Functions |
| title_short | Generalized Fractional Integral Inequalities Derived from Convexity Properties of Twice-Differentiable Functions |
| title_sort | generalized fractional integral inequalities derived from convexity properties of twice differentiable functions |
| topic | generalized fractional operators Hermite–Hadamard inequality convex functions |
| url | https://www.mdpi.com/2504-3110/9/2/97 |
| work_keys_str_mv | AT areejaalmoneef generalizedfractionalintegralinequalitiesderivedfromconvexitypropertiesoftwicedifferentiablefunctions AT abdallahhyder generalizedfractionalintegralinequalitiesderivedfromconvexitypropertiesoftwicedifferentiablefunctions AT fatihhezenci generalizedfractionalintegralinequalitiesderivedfromconvexitypropertiesoftwicedifferentiablefunctions AT huseyinbudak generalizedfractionalintegralinequalitiesderivedfromconvexitypropertiesoftwicedifferentiablefunctions |