Further Midpoint Inequalities via Generalized Fractional Operators in Riemann–Liouville Sense

Hyder, Abd‐Allah; Budak, Hüseyın; Almoneef, Areej A.

doi:10.3390/fractalfract6090496

Cited by 8 publications

(9 citation statements)

References 36 publications

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“…If we substitute from ( 31) and ( 32) in ( 29), we obtain the first inequality of (30). The second inequality of ( 30) is obvious from the inequality (20).…”

Section: Trapezoid Type Inequalitiesmentioning

confidence: 99%

“…Fractional derivatives have been extensively applied in the fractional calculus field and its implications for other scientific disciplines. With great success, Caputo and Riemann-Liouville derivatives were widely employed to describe complicated dynamics in physics, biology, engineering, and plentiful other domains [15][16][17][18][19][20]. It is generally known that systems with a memory impact often occur in natural events.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On New Fractional Version of Generalized Hermite-Hadamard Inequalities

et al. 2022

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In this study, we establish a novel version of Hermite-Hadamard inequalities through neoteric generalized Riemann-Liouville fractional integrals (RLFIs). For functions with the convex absolute values of derivatives, we create a variety of midpoint and trapezoid form inequalities, including the generalized RLFIs. Moreover, multiple fractional inequalities can be produced as special cases of the findings of this study.

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“…If we substitute from ( 31) and ( 32) in ( 29), we obtain the first inequality of (30). The second inequality of ( 30) is obvious from the inequality (20).…”

Section: Trapezoid Type Inequalitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On New Fractional Version of Generalized Hermite-Hadamard Inequalities

et al. 2022

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“…Subsequently, Ostrowski-type inequalities were derived in [28], expanding the toolkit for analyzing this class of fractional integrals. Hyder et al made significant contributions by introducing midpoint-type inequalities in [29]. In [30], Kara et al extended these efforts by providing midpoint-type and trapezoid-type inequalities specifically tailored for twice-differentiable convex functions.…”

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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“…Budak discussed the Ostrowskiiand Simpson'sitype inequalities for differentiable convex function by using the extended fractionaliintegrals in [26]. Recently, a few generic and midpoint-shaped fractional inequalities were explored by Hyder et al (see [27]). Using the well-known fractional operator (Caputo-Fabrizio), Xiaobin wang et al [28] proved the Hermite-Hadamarditype inequalities for modified h-convexifunctions.…”

Section: Introductionmentioning

confidence: 99%

Error Bounds for Fractional Integral Inequalities with Applications

Alqahtani,

Qaisar,

Munir

et al. 2024

Fractal Fract

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Fractional calculus has been a concept used to obtain new variants of some well-known integral inequalities. In this study, our main goal is to establish the new fractional Hermite–Hadamard, and Simpson’s type estimates by employing a differentiable function. Furthermore, a novel class of fractional integral related to prominent fractional operator (Caputo–Fabrizio) for differentiable convex functions of first order is proven. Then, taking this equality into account as an auxiliary result, some new estimation of the Hermite–Hadamard and Simpson’s type inequalities as generalization is presented. Moreover, few inequalities for concave function are obtained as well. It is observed that newly established outcomes are the extension of comparable inequalities existing in the literature. Additionally, we discuss the applications to special means, matrix inequalities, and the q-digamma function.

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Further Midpoint Inequalities via Generalized Fractional Operators in Riemann–Liouville Sense

Cited by 8 publications

References 36 publications

On New Fractional Version of Generalized Hermite-Hadamard Inequalities

On New Fractional Version of Generalized Hermite-Hadamard Inequalities

On Conformable Fractional Milne-Type Inequalities

Error Bounds for Fractional Integral Inequalities with Applications

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