Hermite-Hadamard Fractional Inequalities for Differentiable Functions
In this article, we look at a variety of mean-type integral inequalities for a well-known Hilfer fractional derivative. We consider twice differentiable convex and <i>s</i>-convex functions for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display=&q...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/2/60 |
| _version_ | 1797480112244916224 |
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| author | Muhammad Samraiz Zahida Perveen Gauhar Rahman Muhammad Adil Khan Kottakkaran Sooppy Nisar |
| author_facet | Muhammad Samraiz Zahida Perveen Gauhar Rahman Muhammad Adil Khan Kottakkaran Sooppy Nisar |
| author_sort | Muhammad Samraiz |
| collection | DOAJ |
| description | In this article, we look at a variety of mean-type integral inequalities for a well-known Hilfer fractional derivative. We consider twice differentiable convex and <i>s</i>-convex functions for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></semantics></math></inline-formula> that have applications in optimization theory. In order to infer more interesting mean inequalities, some identities are also established. The consequences for Caputo fractional derivative are presented as special cases to our general conclusions. |
| first_indexed | 2024-03-09T21:55:44Z |
| format | Article |
| id | doaj.art-66bb5d36d76e4bfd9a404d90027f07f4 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T21:55:44Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-66bb5d36d76e4bfd9a404d90027f07f42023-11-23T19:58:32ZengMDPI AGFractal and Fractional2504-31102022-01-01626010.3390/fractalfract6020060Hermite-Hadamard Fractional Inequalities for Differentiable FunctionsMuhammad Samraiz0Zahida Perveen1Gauhar Rahman2Muhammad Adil Khan3Kottakkaran Sooppy Nisar4Department of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematics and Statistics, Hazara University, Mansehra 21300, PakistanDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanDepartment of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawser 11991, Saudi ArabiaIn this article, we look at a variety of mean-type integral inequalities for a well-known Hilfer fractional derivative. We consider twice differentiable convex and <i>s</i>-convex functions for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></semantics></math></inline-formula> that have applications in optimization theory. In order to infer more interesting mean inequalities, some identities are also established. The consequences for Caputo fractional derivative are presented as special cases to our general conclusions.https://www.mdpi.com/2504-3110/6/2/60Hermite-Hadamard-type inequalitiesHilfer fractional derivativeHölder’s inequality |
| spellingShingle | Muhammad Samraiz Zahida Perveen Gauhar Rahman Muhammad Adil Khan Kottakkaran Sooppy Nisar Hermite-Hadamard Fractional Inequalities for Differentiable Functions Fractal and Fractional Hermite-Hadamard-type inequalities Hilfer fractional derivative Hölder’s inequality |
| title | Hermite-Hadamard Fractional Inequalities for Differentiable Functions |
| title_full | Hermite-Hadamard Fractional Inequalities for Differentiable Functions |
| title_fullStr | Hermite-Hadamard Fractional Inequalities for Differentiable Functions |
| title_full_unstemmed | Hermite-Hadamard Fractional Inequalities for Differentiable Functions |
| title_short | Hermite-Hadamard Fractional Inequalities for Differentiable Functions |
| title_sort | hermite hadamard fractional inequalities for differentiable functions |
| topic | Hermite-Hadamard-type inequalities Hilfer fractional derivative Hölder’s inequality |
| url | https://www.mdpi.com/2504-3110/6/2/60 |
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