Some New Bennett–Leindler Type Inequalities via Conformable Fractional Nabla Calculus
In this article, we prove several new fractional nabla Bennett–Leindler dynamic inequalities with the help of a simple consequence of Keller’s chain rule, integration by parts, mean inequalities and Hölder’s inequality for the nabla fractional derivative on time scales. As a result of this, some new...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/10/2183 |
| _version_ | 1797469862544539648 |
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| author | Ghada AlNemer Mohammed Zakarya Roqia Butush Haytham M. Rezk |
| author_facet | Ghada AlNemer Mohammed Zakarya Roqia Butush Haytham M. Rezk |
| author_sort | Ghada AlNemer |
| collection | DOAJ |
| description | In this article, we prove several new fractional nabla Bennett–Leindler dynamic inequalities with the help of a simple consequence of Keller’s chain rule, integration by parts, mean inequalities and Hölder’s inequality for the nabla fractional derivative on time scales. As a result of this, some new classical inequalities are obtained as special cases, and we extended our inequalities to discrete and continuous calculus. In addition, when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, we shall obtain some well-known dynamic inequalities as special instances from our results. Symmetrical properties are critical in determining the best ways to solve inequalities. |
| first_indexed | 2024-03-09T19:26:06Z |
| format | Article |
| id | doaj.art-a8fe733c547442ea8700e5eac8f50625 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T19:26:06Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-a8fe733c547442ea8700e5eac8f506252023-11-24T02:53:52ZengMDPI AGSymmetry2073-89942022-10-011410218310.3390/sym14102183Some New Bennett–Leindler Type Inequalities via Conformable Fractional Nabla CalculusGhada AlNemer0Mohammed Zakarya1Roqia Butush2Haytham M. Rezk3Department 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, University of Jordan, Amman P.O. Box 11941, JordanDepartment of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, EgyptIn this article, we prove several new fractional nabla Bennett–Leindler dynamic inequalities with the help of a simple consequence of Keller’s chain rule, integration by parts, mean inequalities and Hölder’s inequality for the nabla fractional derivative on time scales. As a result of this, some new classical inequalities are obtained as special cases, and we extended our inequalities to discrete and continuous calculus. In addition, when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, we shall obtain some well-known dynamic inequalities as special instances from our results. Symmetrical properties are critical in determining the best ways to solve inequalities.https://www.mdpi.com/2073-8994/14/10/2183nabla derivativeHardy’s inequalityHölder’s inequalitytime scalesconformable fractional calculus |
| spellingShingle | Ghada AlNemer Mohammed Zakarya Roqia Butush Haytham M. Rezk Some New Bennett–Leindler Type Inequalities via Conformable Fractional Nabla Calculus Symmetry nabla derivative Hardy’s inequality Hölder’s inequality time scales conformable fractional calculus |
| title | Some New Bennett–Leindler Type Inequalities via Conformable Fractional Nabla Calculus |
| title_full | Some New Bennett–Leindler Type Inequalities via Conformable Fractional Nabla Calculus |
| title_fullStr | Some New Bennett–Leindler Type Inequalities via Conformable Fractional Nabla Calculus |
| title_full_unstemmed | Some New Bennett–Leindler Type Inequalities via Conformable Fractional Nabla Calculus |
| title_short | Some New Bennett–Leindler Type Inequalities via Conformable Fractional Nabla Calculus |
| title_sort | some new bennett leindler type inequalities via conformable fractional nabla calculus |
| topic | nabla derivative Hardy’s inequality Hölder’s inequality time scales conformable fractional calculus |
| url | https://www.mdpi.com/2073-8994/14/10/2183 |
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