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Search Results (3)

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Keywords = fractional bennett’s inequality

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16 pages, 329 KiB  
Article
Some New Bennett–Leindler Type Inequalities via Conformable Fractional Nabla Calculus
by Ghada AlNemer, Mohammed Zakarya, Roqia Butush and Haytham M. Rezk
Symmetry 2022, 14(10), 2183; https://doi.org/10.3390/sym14102183 - 18 Oct 2022
Cited by 2 | Viewed by 1360
Abstract
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 [...] Read more.
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 α=1, 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. Full article
(This article belongs to the Special Issue Symmetry in New Trends for Discrete Fractional Calculus with Applications)
16 pages, 334 KiB  
Article
Fractional Reverse Coposn’s Inequalities via Conformable Calculus on Time Scales
by Mohammed Zakarya, Mohamed Altanji, Ghada AlNemer, Hoda A. Abd El-Hamid, Clemente Cesarano and Haytham M. Rezk
Symmetry 2021, 13(4), 542; https://doi.org/10.3390/sym13040542 - 25 Mar 2021
Cited by 24 | Viewed by 2019
Abstract
This paper provides novel generalizations by considering the generalized conformable fractional integrals for reverse Copson’s type inequalities on time scales. The main results will be proved using a general algebraic inequality, chain rule, Hölder’s inequality, and integration by parts on fractional time scales. [...] Read more.
This paper provides novel generalizations by considering the generalized conformable fractional integrals for reverse Copson’s type inequalities on time scales. The main results will be proved using a general algebraic inequality, chain rule, Hölder’s inequality, and integration by parts on fractional time scales. Our investigations unify and extend some continuous inequalities and their corresponding discrete analogues. In addition, when α = 1, we obtain some well-known time scale inequalities due to Hardy, Copson, Bennett, and Leindler inequalities. Full article
(This article belongs to the Special Issue Complex Variable in Approximation Theory)
15 pages, 280 KiB  
Article
Some Fractional Dynamic Inequalities of Hardy’s Type via Conformable Calculus
by Samir Saker, Mohammed Kenawy, Ghada AlNemer and Mohammed Zakarya
Mathematics 2020, 8(3), 434; https://doi.org/10.3390/math8030434 - 16 Mar 2020
Cited by 28 | Viewed by 3002
Abstract
In this article, we prove some new fractional dynamic inequalities on time scales via conformable calculus. By using chain rule and Hölder’s inequality on timescales we establish the main results. When α = 1 we obtain some well-known time-scale inequalities due to Hardy, [...] Read more.
In this article, we prove some new fractional dynamic inequalities on time scales via conformable calculus. By using chain rule and Hölder’s inequality on timescales we establish the main results. When α = 1 we obtain some well-known time-scale inequalities due to Hardy, Copson, Bennett and Leindler inequalities. Full article
(This article belongs to the Special Issue Fractional Differential Equations, Inclusions and Inequalities with Applications)
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