Conformable fractional versions of Hermite–Hadamard-type inequalities for twice-differentiable functions

Hezenci, Fatih; Kara, Hasan; Budak, Hüseyın

doi:10.1186/s13661-023-01737-y

Cited by 5 publications

(1 citation statement)

References 22 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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New Fractional Inequalities through Convex Functions and Comprehensive Riemann–Liouville Integrals

Hyder

2023

Journal of Mathematics

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In most fields of applied sciences, inequalities are important in constructing mathematical systems and associated solution functions. Convexity also has a significant impact on an assortment of mathematical topics. By utilizing a comprehensive version of Riemann–Liouville integrals and the functions’ convexity condition, we present and prove novel fractional inequalities. According to the current literature, this work is a novel addition to the literature, and the proposed technique for addressing fractional inequalities issues is straightforward and simple to execute. It is also easy to see that all of the inequalities that have been developed are inclusive and may be reduced to a variety of other inequalities that have been proposed in the literature. Additionally, certain numeric examples with graphs are provided to support the theoretical results.

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New midpoint-type inequalities in the context of the proportional Caputo-hybrid operator

Demir,

Tunç

2024

J Inequal Appl

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Fractional calculus is a crucial foundation in mathematics and applied sciences, serving as an extremely valuable tool. Besides, the new hybrid fractional operator, which combines proportional and Caputo operators, offers better applications in numerous fields of mathematics and computer sciences. Due to its wide range of applications, we focus on the proportional Caputo-hybrid operator in this research article. Firstly, we begin by establishing a novel identity for this operator. Then, based on the newfound identity, we establish some integral inequalities that are relevant to the left-hand side of Hermite–Hadamard-type inequalities for the proportional Caputo-hybrid operator. Furthermore, we show how the results improve upon and refine many previous findings in the setting of integral inequalities. Later, we present specific examples together with their related graphs to offer a better understanding of the newly obtained inequalities. Our results not only extend previous studies but also provide valuable viewpoints and methods for tackling a wide range of mathematical and scientific problems.

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Conformable fractional versions of Hermite–Hadamard-type inequalities for twice-differentiable functions

Cited by 5 publications

References 22 publications

On Conformable Fractional Milne-Type Inequalities

On Conformable Fractional Milne-Type Inequalities

New Fractional Inequalities through Convex Functions and Comprehensive Riemann–Liouville Integrals

New midpoint-type inequalities in the context of the proportional Caputo-hybrid operator

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