scholarly journals On new general versions of Hermite–Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Havva Kavurmacı Önalan ◽  
Ahmet Ocak Akdemir ◽  
Merve Avcı Ardıç ◽  
Dumitru Baleanu
Keyword(s):  
Integral Equation ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Frequency Of Use ◽  
Second Derivatives ◽  
New Variant ◽  
Type Integral ◽  
Basic Concepts

AbstractThe main motivation of this study is to bring together the field of inequalities with fractional integral operators, which are the focus of attention among fractional integral operators with their features and frequency of use. For this purpose, after introducing some basic concepts, a new variant of Hermite–Hadamard (HH-) inequality is obtained for s-convex functions in the second sense. Then, an integral equation, which is important for the main findings, is proved. With the help of this integral equation that includes fractional integral operators with Mittag-Leffler kernel, many HH-type integral inequalities are derived for the functions whose absolute values of the second derivatives are s-convex and s-concave. Some classical inequalities and hypothesis conditions, such as Hölder’s inequality and Young’s inequality, are taken into account in the proof of the findings.

scholarly journals Certain Chebyshev Type Integral Inequalities Involving Hadamard’s Fractional Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Sotiris K. Ntouyas ◽  
Sunil D. Purohit ◽  
Jessada Tariboon
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Weighted Version ◽  
Fractional Integral Operators ◽  
Differentiable Functions ◽  
Type Integral ◽  
Chebyshev Functional

We establish certain new fractional integral inequalities for the differentiable functions whose derivatives belong to the spaceLp([1,∞)), related to the weighted version of the Chebyshev functional, involving Hadamard’s fractional integral operators. As an application, particular results have been also established.

New Hadamard-type integral inequalities via a general form of fractional integral operators

2021 ◽  
Vol 148 ◽  
pp. 111025
Author(s):  
Saad Ihsan Butt ◽  
Saba Yousaf ◽  
Ahmet Ocak Akdemir ◽  
Mustafa Ali Dokuyucu
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Type Integral

scholarly journals Some Hermite–Hadamard and Ostrowski type inequalities for fractional integral operators with exponential kernel

2019 ◽  
Vol 23 (1) ◽  
pp. 25-36
Author(s):  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya ◽  
Fuat Usta ◽  
Hüseyin Yildirim
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Exponential Kernel ◽  
Power Means ◽  
Type Integral

We rstly establish Hermite–Hadamard type integral inequalities for fractional integral operators. Secondly, we give new generalizations of fractional Ostrowski type inequalities through convex functions via Hölder and power means inequalities. In accordance with this purpose, we use fractional integral operators with exponential kernel.

Chebyshev type inequality containing a fractional integral operator with a multi-index Mittag-Leffler function as a kernel

Analysis ◽  
2021 ◽  
Vol 41 (1) ◽  
pp. 61-67
Author(s):  
Kamlesh Jangid ◽  
S. D. Purohit ◽  
Kottakkaran Sooppy Nisar ◽  
Serkan Araci
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Type Inequality ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Multi Index ◽  
Type Integral ◽  
Special Case

Abstract In this paper, we derive certain Chebyshev type integral inequalities connected with a fractional integral operator in terms of the generalized Mittag-Leffler multi-index function as a kernel. Our key findings are general in nature and, as a special case, can give rise to integral inequalities of the Chebyshev form involving fractional integral operators present in the literature.

scholarly journals On integral inequalities related to the weighted and the extended Chebyshev functionals involving different fractional operators

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Barış Çelik ◽  
Mustafa Ç. Gürbüz ◽  
M. Emin Özdemir ◽  
Erhan Set
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Fractional Integral Operators

AbstractThe role of fractional integral operators can be found as one of the best ways to generalize classical inequalities. In this paper, we use different fractional integral operators to produce some inequalities for the weighted and the extended Chebyshev functionals. The results are more general than the available classical results in the literature.

scholarly journals On certain new CAUCHY–TYPE fracitioanl integral inequalities and OPIAL–TYPE fractional derivative inequalities

2015 ◽  
Vol 46 (1) ◽  
pp. 67-73 ◽  
Author(s):  
Amit Chouhan
Keyword(s):  
Fractional Derivative ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Future Research ◽  
Cauchy Type ◽  
Fractional Integral Operators ◽  
Integrable Functions ◽  
New Inequalities

The aim of this paper is to establish several new fractional integral and derivative inequalities for non-negative and integrable functions. These inequalities related to the extension of general Cauchy type inequalities and involving Saigo, Riemann-Louville type fractional integral operators together with multiple Erdelyi-Kober operator. Furthermore the Opial-type fractional derivative inequality involving H-function is also established. The generosity of H-function could leads to several new inequalities that are of great interest of future research.

scholarly journals Inequalities by Means of Generalized Proportional Fractional Integral Operators with Respect to Another Function

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1225 ◽  
Author(s):  
Saima Rashid ◽  
Fahd Jarad ◽  
Muhammad Aslam Noor ◽  
Humaira Kalsoom ◽  
Yu-Ming Chu
Keyword(s):  
Real World ◽  
Fractional Integral ◽  
Numerical Approximation ◽  
Integral Operators ◽  
Integral Inequalities ◽  
The Novel ◽  
Fractional Integral Operators ◽  
Real World Problems

In this article, we define a new fractional technique which is known as generalized proportional fractional (GPF) integral in the sense of another function Ψ . The authors prove several inequalities for newly defined GPF-integral with respect to another function Ψ . Our consequences will give noted outcomes for a suitable variation to the GPF-integral in the sense of another function Ψ and the proportionality index ς . Furthermore, we present the application of the novel operator with several integral inequalities. A few new properties are exhibited, and the numerical approximation of these new operators is introduced with certain utilities to real-world problems.

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