Caputo–Fabrizio fractional Hermite–Hadamard type and associated results for strongly convex functions

Nwaeze, Eze R.; Kermausuor, Seth

doi:10.1007/s41478-021-00315-8

Cited by 6 publications

(2 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Sahoo et al [13,14] developed Hermite-Hadamard and midpoint inequalities via Caputo-Fabrizio operator. Nwaeze et al [15] established these inequalities using strongly convex mappings. Utilizing h-convexity, Cortez et al [16] created Hermite-Hadamard Mercer-type inequalities using the Caputo-Fabrizio operator.…”

Section: Introductionmentioning

confidence: 99%

Hermite–Hadamard-Type Inequalities via Caputo–Fabrizio Fractional Integral for h-Godunova–Levin and (h1, h2)-Convex Functions

Afzal,

Abbas,

Hamali

et al. 2023

Fractal Fract

View full text Add to dashboard Cite

This note generalizes several existing results related to Hermite–Hadamard inequality using h-Godunova–Levin and (h1,h2)-convex functions using a fractional integral operator associated with the Caputo–Fabrizio fractional derivative. This study uses a non-singular kernel and constructs some new theorems associated with fractional order integrals. Furthermore, we demonstrate that the obtained results are a generalization of the existing ones. To demonstrate the correctness of these results, we developed a few interesting non-trivial examples. Finally, we discuss some applications of our findings associated with special means.

show abstract

Section: Introductionmentioning

confidence: 99%

Hermite–Hadamard-Type Inequalities via Caputo–Fabrizio Fractional Integral for h-Godunova–Levin and (h1, h2)-Convex Functions

Afzal,

Abbas,

Hamali

et al. 2023

Fractal Fract

View full text Add to dashboard Cite

show abstract

“…Butt and his collaborators, for example, worked on Jensen-Mercer type inequalities using novel fractional operators (see [27][28][29]), while Set et al [30] and Fernandez et al [31] presented the Hermite-Hadamard inequality using the Atangana-Baleanu fractional operator. For some recent generalizations of the Hermite-Hadamard inequality, we suggest interested readers to see [32][33][34][35][36] and the references therein. Recently, Naila et al [37] presented some results for tgs-convex function via fractional calculus.…”

Section: Introductionmentioning

confidence: 99%

Integral Inequalities of Integer and Fractional Orders for n–Polynomial Harmonically tgs–Convex Functions and Their Applications

Kashuri

Sahoo

Kodamasingh

et al. 2022

Journal of Mathematics

View full text Add to dashboard Cite

The main objective of this article is to introduce the notion of n –polynomial harmonically t g s –convex function and study its algebraic properties. First, we use this notion to present new variants of the Hermite–Hadamard type inequality and related integral inequalities, as well as their fractional analogues. Further, we prove two interesting integral and fractional identities for differentiable mappings, and, using them as auxiliary results, some refinements of Hermite–Hadamard type integral inequalities for both classical and fractional versions are presented. Finally, in order to show the efficiency of our results, some applications for special means and error estimations are obtained as well.

show abstract

Midpoint-type integral inequalities for ( s , m )-convex functions in the third sense involving Caputo fractional derivatives and Caputo–Fabrizio integrals

Khan,

Ikram,

Nosheen

et al. 2024

Applied Mathematics in Science and Engineering

View full text Add to dashboard Cite

Caputo–Fabrizio fractional Hermite–Hadamard type and associated results for strongly convex functions

Cited by 6 publications

References 29 publications

Hermite–Hadamard-Type Inequalities via Caputo–Fabrizio Fractional Integral for h-Godunova–Levin and (h1, h2)-Convex Functions

Hermite–Hadamard-Type Inequalities via Caputo–Fabrizio Fractional Integral for h-Godunova–Levin and (h1, h2)-Convex Functions

Integral Inequalities of Integer and Fractional Orders for n–Polynomial Harmonically tgs–Convex Functions and Their Applications

Midpoint-type integral inequalities for ( s , m )-convex functions in the third sense involving Caputo fractional derivatives and Caputo–Fabrizio integrals

Contact Info

Product

Resources

About