Hardy-Leindler-Type Inequalities via Conformable Delta Fractional Calculus

Rezk, Haytham M.; Albalawi, Wedad; El-Hamid, H. A. Abd; Saied, Ahmed I.; Bazighifan, Omar; Mohamed, Mohamed S.; Zakarya, Mohammed

doi:10.1155/2022/2399182

Cited by 8 publications

(3 citation statements)

References 15 publications

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“…These efforts have collectively contributed to a comprehensive understanding of inequalities related to conformable fractional integrals. For those interested in delving further into this topic, additional related works are available for reference in [39][40][41][42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

On Conformable Fractional Milne-Type Inequalities

Ying,

Lakhdari,

et al. 2024

Symmetry

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Building upon previous research in conformable fractional calculus, this study introduces a novel identity. Using this identity as a foundation, we derive a set of conformable fractional Milne-type inequalities specifically designed for differentiable convex functions. The obtained results recover some existing inequalities in the literature by fixing some parameters. These novel contributions aim to enrich the analytical tools available for studying convex functions within the realm of conformable fractional calculus. The derived inequalities reflect an inherent symmetry characteristic of the Milne formula, further illustrating the balanced and harmonious mathematical structure within these frameworks. We provide a thorough example with graphical representations to support our findings, offering both numerical insights and visual confirmation of the established inequalities.

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Section: Introductionmentioning

confidence: 99%

On Conformable Fractional Milne-Type Inequalities

Ying,

Lakhdari,

et al. 2024

Symmetry

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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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“…In recent years, by utilizing the conformable calculus, many authors proved several results related to some integral inequalities like Chebyshev type inequality [3], Hardy type inequalities [25], Hermite-Hadamard type inequalities [2,12,13], and Iyengar type inequalities [27]. For more details of conformable calculus we refer the reader to the papers [10,14,15,21,22,29] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%