Some New Harmonically Convex Function Type Generalized Fractional Integral Inequalities

Ali, Rana Safdar; Mukheimer, Aiman; Abdeljawad, Thabet; Mubeen, Shahid; Ali, Sabila; Rahman, Gauhar; Nisar, Kottakkaran Sooppy

doi:10.3390/fractalfract5020054

Cited by 10 publications

(3 citation statements)

References 22 publications

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“…Due to broad utility of Hermite-Hadamard inequalities and fractional calculus, and across various scientific disciplines, researchers are actively exploring these type of inequalities. This research direction has gained momentum, as evidenced by recent developments in the field (see e.g., [12][13][14][15][16][17]). Sarikaya et al,in [18] established the Hermite-Hadamard type inequalities for fractional integrals:…”

Section: Definitionmentioning

confidence: 99%

Some New Fractional Inequalities Defined Using cr-Log-h-Convex Functions and Applications

Mehmood,

Mohammed,

Kashuri

et al. 2024

Symmetry

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There is a strong correlation between the concept of convexity and symmetry. One of these is the class of interval-valued cr-log-h-convex functions, which is closely related to the theory of symmetry. In this paper, we obtain Hermite–Hadamard and its weighted version inequalities that are related to interval-valued cr-log-h-convex functions, and some known results are recaptured. To support our main results, we offer three examples and two applications related to modified Bessel functions and special means as well.

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Section: Definitionmentioning

confidence: 99%

Some New Fractional Inequalities Defined Using cr-Log-h-Convex Functions and Applications

Mehmood,

Mohammed,

Kashuri

et al. 2024

Symmetry

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show abstract

“…The main focus of this article to study the correlation between mathematical inequality and fractional operators. The improvements of fractional operators are backed by presenting different types of inequalities such as H -H type [26,27], Minkowski type [28,29], Grüss type [30,31], Pólya-Szegö type [32], and Chebyshev type [33] employing these operators. Lately, many mathematicians have incorporated the concepts of new notions of fractional integrals and well-known inequalities.…”

Section: Definition 11 ([1]) a Functionmentioning

confidence: 99%

Ostrowski-type inequalities pertaining to Atangana–Baleanu fractional operators and applications containing special functions

et al. 2022

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The objective of this article is to incorporate the concept of the Ostrowski inequality with the Atangana–Baleanu fractional integral operator. A novel integral identity for twice-differentiable functions is established after a rigorous investigation of several basic definitions and existing ideas related to inequalities and fractional calculus. Following that, numerous Ostrowski-type inequalities are provided based on this identity, which uses Mittag–Leffler as its kernel structure. Some specific applications, such as q-digamma functions and modified Bessel functions, are also investigated. Choosing $s=1$ s = 1 , we also analyze new results for convex functions as special cases. Our findings corroborate some well-documented inequalities.

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“…Based on this identity, certain Simpson-like type inequality fndings are found. Te authors of [25] created a novel form of extended fractional Hadamard and Fejér-Hadamard form integral inequalities. Te conclusion of [26] is to use a novel technique to derive limits for sums of left and right proportional fractional integrals of a generic kind, as well as other associated inequalities.…”

Section: Introductionmentioning

confidence: 99%

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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Some New Harmonically Convex Function Type Generalized Fractional Integral Inequalities

Cited by 10 publications

References 22 publications

Some New Fractional Inequalities Defined Using cr-Log-h-Convex Functions and Applications

Some New Fractional Inequalities Defined Using cr-Log-h-Convex Functions and Applications

Ostrowski-type inequalities pertaining to Atangana–Baleanu fractional operators and applications containing special functions

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

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