Certain fractional inequalities via the Caputo Fabrizio operator-Reference-Cited by-同舟云学术

Certain fractional inequalities via the Caputo Fabrizio operator

Published:2023 Issue:29 Volume:37 Page:10093-10106
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Qaisar Shahid¹,Munir Arslan¹,Budak Hüseyin²

Affiliation:

1. Department of Mathematics, COMSATS University Islamabad, Sahiwal Campus, Sahiwal, Pakistan

2. Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Türkiye

Abstract

The Caputo Fabrizio fractional integral operator is one of the key concepts in fractional calculus. It is involved in many concrete and practical issues. In the present study, we have discussed some novel ideas to fractional Hermite-Hadamard inequalities within a Caputo Fabrizio fractional integral framework. The fractional integral under investigation is used to establish some new fractional Hermite-Hadamard inequalities. The findings of this study can be seen as a generalization and extension of numerous earlier inequalities via convex function. In addition, we demonstrate a few applications of our findings to special means of real numbers.

Publisher

National Library of Serbia

Reference39 articles.

1. Diethelm, K.: The Analysis of Fractional Differential Equations: AnApplication-Oriented Exposition Using Differential Operators of Caputo Type. Springer, Berlin (2010).

2. Hadamard, J. Étude sur les propriétés des fonctions enti`eres en particulier d’une fonction considérée par Riemann. J. Math. Pures Appl. 1893, 58, 171-215

3. Alomari, M.; Darus, M.; Kirmaci, U.S. Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means. Comput. Math. Appl. 2010, 59, 225-232.

4. Mumcu, I.; Set, E.; Akdemir, A.O.; Jarad, F. New extensions of Hermite-Hadamard inequalities via generalized proportional fractional integral. Numer. Methods Partial Differ. Equ. 2021, 1-12.

5. Liu, K.; Wang, J.; O’Regan, D. On the Hermite-Hadamard type inequality for -Riemann-Liouville fractional integrals via convex functions. J. Inequal. Appl. 2019, 27.