New Fractional Integral Inequalities Pertaining to Caputo–Fabrizio and Generalized Riemann–Liouville Fractional Integral Operators
Integral inequalities have accumulated a comprehensive and prolific field of research within mathematical interpretations. In recent times, strategies of fractional calculus have become the subject of intensive research in historical and contemporary generations because of their applications in vari...
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MDPI AG
2022-11-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/11/618 |
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| author | Muhammad Tariq Omar Mutab Alsalami Asif Ali Shaikh Kamsing Nonlaopon Sotiris K. Ntouyas |
| author_facet | Muhammad Tariq Omar Mutab Alsalami Asif Ali Shaikh Kamsing Nonlaopon Sotiris K. Ntouyas |
| author_sort | Muhammad Tariq |
| collection | DOAJ |
| description | Integral inequalities have accumulated a comprehensive and prolific field of research within mathematical interpretations. In recent times, strategies of fractional calculus have become the subject of intensive research in historical and contemporary generations because of their applications in various branches of science. In this paper, we concentrate on establishing Hermite–Hadamard and Pachpatte-type integral inequalities with the aid of two different fractional operators. In particular, we acknowledge the critical Hermite–Hadamard and related inequalities for <i>n</i>-polynomial <i>s</i>-type convex functions and <i>n</i>-polynomial <i>s</i>-type harmonically convex functions. We practice these inequalities to consider the Caputo–Fabrizio and the <i>k</i>-Riemann–Liouville fractional integrals. Several special cases of our main results are also presented in the form of corollaries and remarks. Our study offers a better perception of integral inequalities involving fractional operators. |
| first_indexed | 2024-03-09T19:16:24Z |
| format | Article |
| id | doaj.art-a9d88244146340709a7b2b7c8575d624 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T19:16:24Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-a9d88244146340709a7b2b7c8575d6242023-11-24T03:44:22ZengMDPI AGAxioms2075-16802022-11-01111161810.3390/axioms11110618New Fractional Integral Inequalities Pertaining to Caputo–Fabrizio and Generalized Riemann–Liouville Fractional Integral OperatorsMuhammad Tariq0Omar Mutab Alsalami1Asif Ali Shaikh2Kamsing Nonlaopon3Sotiris K. Ntouyas4Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, PakistanDepartment of Electrical Engineering, College of Engineering, Taif University, Taif 21944, Saudi ArabiaDepartment of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, PakistanDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mathematics, University of Ioannina, 451 10 Ioannina, GreeceIntegral inequalities have accumulated a comprehensive and prolific field of research within mathematical interpretations. In recent times, strategies of fractional calculus have become the subject of intensive research in historical and contemporary generations because of their applications in various branches of science. In this paper, we concentrate on establishing Hermite–Hadamard and Pachpatte-type integral inequalities with the aid of two different fractional operators. In particular, we acknowledge the critical Hermite–Hadamard and related inequalities for <i>n</i>-polynomial <i>s</i>-type convex functions and <i>n</i>-polynomial <i>s</i>-type harmonically convex functions. We practice these inequalities to consider the Caputo–Fabrizio and the <i>k</i>-Riemann–Liouville fractional integrals. Several special cases of our main results are also presented in the form of corollaries and remarks. Our study offers a better perception of integral inequalities involving fractional operators.https://www.mdpi.com/2075-1680/11/11/618Hermite–Hadamard inequalityconvex functionharmonically convex functionCaputo–Fabrizio fractional operatorfractional integral inequality |
| spellingShingle | Muhammad Tariq Omar Mutab Alsalami Asif Ali Shaikh Kamsing Nonlaopon Sotiris K. Ntouyas New Fractional Integral Inequalities Pertaining to Caputo–Fabrizio and Generalized Riemann–Liouville Fractional Integral Operators Axioms Hermite–Hadamard inequality convex function harmonically convex function Caputo–Fabrizio fractional operator fractional integral inequality |
| title | New Fractional Integral Inequalities Pertaining to Caputo–Fabrizio and Generalized Riemann–Liouville Fractional Integral Operators |
| title_full | New Fractional Integral Inequalities Pertaining to Caputo–Fabrizio and Generalized Riemann–Liouville Fractional Integral Operators |
| title_fullStr | New Fractional Integral Inequalities Pertaining to Caputo–Fabrizio and Generalized Riemann–Liouville Fractional Integral Operators |
| title_full_unstemmed | New Fractional Integral Inequalities Pertaining to Caputo–Fabrizio and Generalized Riemann–Liouville Fractional Integral Operators |
| title_short | New Fractional Integral Inequalities Pertaining to Caputo–Fabrizio and Generalized Riemann–Liouville Fractional Integral Operators |
| title_sort | new fractional integral inequalities pertaining to caputo fabrizio and generalized riemann liouville fractional integral operators |
| topic | Hermite–Hadamard inequality convex function harmonically convex function Caputo–Fabrizio fractional operator fractional integral inequality |
| url | https://www.mdpi.com/2075-1680/11/11/618 |
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