On Caputo Fractional Derivatives and Caputo–Fabrizio Integral Operators via (s, m)-Convex Functions-Reference-Cited by-同舟云学术

On Caputo Fractional Derivatives and Caputo–Fabrizio Integral Operators via (s, m)-Convex Functions

Published:2023-02-13 Issue:2 Volume:7 Page:187
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Nosheen Ammara¹^ORCID,Tariq Maria¹,Khan Khuram Ali¹^ORCID,Shah Nehad Ali²,Chung Jae Dong²^ORCID

Affiliation:

1. Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan

2. Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea

Abstract

This paper contains a variety of new integral inequalities for (s,m)-convex functions using Caputo fractional derivatives and Caputo–Fabrizio integral operators. Various generalizations of Hermite–Hadamard-type inequalities containing Caputo–Fabrizio integral operators are derived for those functions whose derivatives are (s,m)-convex. Inequalities involving the digamma function and special means are deduced as applications.

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/2/187/pdf

Reference43 articles.

1. Cloud, M.J., Drachman, B.C., and Lebedev, L.P. (2014). Inequalities with Applications to Engineering, Springer.

2. Some improvements of Jensen’s inequality via 4-convexity and applications;Ullah;J. Funct. Spaces,2022

3. Borwein, J., and Lewi, A. (2000). Convex Analysis and Nonlinear Optimization, Theory and Examples, Springer.

4. Estimations of the Slater Gap via Convexity and Its Applications in Information Theory;Khan;Math. Probl. Eng.,2022

5. Estimation of Jensen’s gap through an integral identity with applications to divergence;Khan;Innov. J. Math.,2022

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Midpoint-type integral inequalities for ( s , m )-convex functions in the third sense involving Caputo fractional derivatives and Caputo–Fabrizio integrals;Applied Mathematics in Science and Engineering;2024-09-12

2. Design of a discrete memristive chaotic map: fractional-order memory, dynamics and application;Physica Scripta;2024-08-08

3. A novel definition of the caputo fractional finite difference approach for Maxwell fluid;Computational and Applied Mathematics;2024-05-14

4. Inequalities presenting error bounds for trapezoidal formula using Caputo-Fabrizio integrals via convex functions with graphical depiction;Journal of Mathematics and Computer Science;2024-02-23

5. Some novel inequalities for Caputo Fabrizio fractional integrals involving (α,s)-convex functions with applications;Mathematical and Computer Modelling of Dynamical Systems;2024-01-09