New Fractional Integral Inequalities for Convex Functions Pertaining to Caputo–Fabrizio Operator
In this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type inequality via a new fractional integral operator associated with the Caputo–Fabrizio derivative are presented. Furthermore, a new fractional identity for differentiable convex functions of first order is pro...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/3/171 |
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| author | Soubhagya Kumar Sahoo Pshtiwan Othman Mohammed Bibhakar Kodamasingh Muhammad Tariq Y. S. Hamed |
| author_facet | Soubhagya Kumar Sahoo Pshtiwan Othman Mohammed Bibhakar Kodamasingh Muhammad Tariq Y. S. Hamed |
| author_sort | Soubhagya Kumar Sahoo |
| collection | DOAJ |
| description | In this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type inequality via a new fractional integral operator associated with the Caputo–Fabrizio derivative are presented. Furthermore, a new fractional identity for differentiable convex functions of first order is proved. Then, taking this identity into account as an auxiliary result and with the assistance of Hölder, power-mean, Young, and Jensen inequality, some new estimations of the Hermite-Hadamard <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="normal">H</mi><mo>-</mo><mi mathvariant="normal">H</mi><mo>)</mo></mrow></semantics></math></inline-formula> type inequality as refinements are presented. Applications to special means and trapezoidal quadrature formula are presented to verify the accuracy of the results. Finally, a brief conclusion and future scopes are discussed. |
| first_indexed | 2024-03-09T19:49:41Z |
| format | Article |
| id | doaj.art-e01d83c0083246d09e797fd6cd593cae |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T19:49:41Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-e01d83c0083246d09e797fd6cd593cae2023-11-24T01:14:51ZengMDPI AGFractal and Fractional2504-31102022-03-016317110.3390/fractalfract6030171New Fractional Integral Inequalities for Convex Functions Pertaining to Caputo–Fabrizio OperatorSoubhagya Kumar Sahoo0Pshtiwan Othman Mohammed1Bibhakar Kodamasingh2Muhammad Tariq3Y. S. Hamed4Department of Mathematics, Institute of Technical Education and Research, Siksha O Anusandhan University, Bhubaneswar 751030, IndiaDepartment of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, IraqDepartment of Mathematics, Institute of Technical Education and Research, Siksha O Anusandhan University, Bhubaneswar 751030, IndiaDepartment of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, PakistanDepartment of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaIn this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type inequality via a new fractional integral operator associated with the Caputo–Fabrizio derivative are presented. Furthermore, a new fractional identity for differentiable convex functions of first order is proved. Then, taking this identity into account as an auxiliary result and with the assistance of Hölder, power-mean, Young, and Jensen inequality, some new estimations of the Hermite-Hadamard <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="normal">H</mi><mo>-</mo><mi mathvariant="normal">H</mi><mo>)</mo></mrow></semantics></math></inline-formula> type inequality as refinements are presented. Applications to special means and trapezoidal quadrature formula are presented to verify the accuracy of the results. Finally, a brief conclusion and future scopes are discussed.https://www.mdpi.com/2504-3110/6/3/171Hermite-Hadamard inequalityCaputo-Fabrizio operatorPachpatte type inequalityHölder’s inequalityHölder-İşcan inequality |
| spellingShingle | Soubhagya Kumar Sahoo Pshtiwan Othman Mohammed Bibhakar Kodamasingh Muhammad Tariq Y. S. Hamed New Fractional Integral Inequalities for Convex Functions Pertaining to Caputo–Fabrizio Operator Fractal and Fractional Hermite-Hadamard inequality Caputo-Fabrizio operator Pachpatte type inequality Hölder’s inequality Hölder-İşcan inequality |
| title | New Fractional Integral Inequalities for Convex Functions Pertaining to Caputo–Fabrizio Operator |
| title_full | New Fractional Integral Inequalities for Convex Functions Pertaining to Caputo–Fabrizio Operator |
| title_fullStr | New Fractional Integral Inequalities for Convex Functions Pertaining to Caputo–Fabrizio Operator |
| title_full_unstemmed | New Fractional Integral Inequalities for Convex Functions Pertaining to Caputo–Fabrizio Operator |
| title_short | New Fractional Integral Inequalities for Convex Functions Pertaining to Caputo–Fabrizio Operator |
| title_sort | new fractional integral inequalities for convex functions pertaining to caputo fabrizio operator |
| topic | Hermite-Hadamard inequality Caputo-Fabrizio operator Pachpatte type inequality Hölder’s inequality Hölder-İşcan inequality |
| url | https://www.mdpi.com/2504-3110/6/3/171 |
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