Generalizations of Hardy’s Type Inequalities via Conformable Calculus

AlNemer, Ghada; Kenawy, Mohammed; Zakarya, Mohammed; Cesarano, Clemente; Rezk, Haytham M.

doi:10.3390/sym13020242

Cited by 11 publications

(9 citation statements)

References 23 publications

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“…Here, we will exemplify our major results in this article. In the pursuing theorem, we will exemplify Leindler's inequality (7) for fractional time scales as follows.…”

Section: Resultsmentioning

confidence: 99%

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Hardy-Leindler-Type Inequalities via Conformable Delta Fractional Calculus

Rezk

Albalawi

El-Hamid

et al. 2022

Journal of Function Spaces

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In this article, some fractional Hardy-Leindler-type inequalities will be illustrated by utilizing the chain law, Hölder’s inequality, and integration by parts on fractional time scales. As a result of this, some classical integral inequalities will be obtained. Also, we would have a variety of well-known dynamic inequalities as special cases from our outcomes when α = 1 .

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“…Here, we will exemplify our major results in this article. In the pursuing theorem, we will exemplify Leindler's inequality (7) for fractional time scales as follows.…”

Section: Resultsmentioning

confidence: 99%

“…which are the time scale version for ( 5) and ( 6), respectively. For developing dynamic inequalities, see the papers ( [6][7][8][9][10][11]). Our target in this article is proving some fractional dynamic inequalities for Hardy-Leindler's type, and it is reversed with employing conformable calculus on time scales.…”

Section: Introductionmentioning

confidence: 99%

Hardy-Leindler-Type Inequalities via Conformable Delta Fractional Calculus

Rezk

Albalawi

El-Hamid

et al. 2022

Journal of Function Spaces

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“…Erturk et al [36] developed a unique Caputo fractional derivative for the corneal shape model of the human eye. The recent literature shows the application of fractional calculus, which can be found in the following references [37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Artificial Neural Network Solution for a Fractional-Order Human Skull Model Using a Hybrid Cuckoo Search Algorithm

Waseem,

Ali,

Khattak

et al. 2023

Symmetry

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In this study, a new fractional-order model for human skull heat conduction is tackled by using a neural network, and the results were further modified by using the hybrid cuckoo search algorithm. In order to understand the temperature distribution, we introduced memory effects into our model by using fractional time derivatives. The objective function was constructed in such a way that the L2−error remained at a minimum. The fractional order equation was then calculated by using the proposed biogeography-based hybrid cuckoo search (BHCS) algorithm to approximate the solution. When compared to earlier simulations based on integer-order models, this method enabled us to examine the fractional-order (FO) cases, as well as the integer order. The results are presented in the form of figures and tables for the different case studies. The results obtained for the various parameters were validated numerically against the available literature, where our proposed methodology showed better performance when compared to the least squares method (LSM).

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“…The study of Hardy-type inequalities attracted and still attracts the attention of many researchers. Over several decades many generalizations, extensions, and refinements have been made to the above inequalities, we refer the interested reader to the papers [1,8,9,18,19,23,24,35,36,41,44], see also [2,21,22,24] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

On nabla conformable fractional Hardy-type inequalities on arbitrary time scales

et al. 2021

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The main aim of the present article is to introduce some new ∇-conformable dynamic inequalities of Hardy type on time scales. We present and prove several results using chain rule and Fubini’s theorem on time scales. Our results generalize, complement, and extend existing results in the literature. Many special cases of the proposed results, such as new conformable fractional h-sum inequalities, new conformable fractional q-sum inequalities, and new classical conformable fractional integral inequalities, are obtained and analyzed.

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Generalizations of Hardy’s Type Inequalities via Conformable Calculus

Abstract: In this paper, we derive some new fractional extensions of Hardy’s type inequalities. The corresponding reverse relations are also obtained by using the conformable fractional calculus from which the classical integral inequalities are deduced as special cases at α=1.

Cited by 11 publications

References 23 publications

Hardy-Leindler-Type Inequalities via Conformable Delta Fractional Calculus

Hardy-Leindler-Type Inequalities via Conformable Delta Fractional Calculus

Artificial Neural Network Solution for a Fractional-Order Human Skull Model Using a Hybrid Cuckoo Search Algorithm

On nabla conformable fractional Hardy-type inequalities on arbitrary time scales

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