scholarly journals On New Generalizations of Hermite-Hadamard Type Inequalities via Atangana-Baleanu Fractional Integral Operators

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 223
Author(s):  
Erhan Set ◽  
Ahmet Ocak Akdemir ◽  
Ali Karaoǧlan ◽  
Thabet Abdeljawad ◽  
Wasfi Shatanawi
Keyword(s):  
Applied Sciences ◽  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Fractional Operators ◽  
Hadamard Inequality ◽  
Fractional Integral Operators ◽  
Inequality Theory ◽  
Fractional Analysis

Fractional operators are one of the frequently used tools to obtain new generalizations of clasical inequalities in recent years and many new fractional operators are defined in the literature. This development in the field of fractional analysis has led to a new orientation in various branches of mathematics and in many of the applied sciences. Thanks to this orientation, it has brought a whole new dimension to the field of inequality theory as well as many other disciplines. In this study, a new lemma has been proved for the fractional integral operator defined by Atangana and Baleanu. Later with the help of this lemma and known inequalities such as Young, Jensen, Hölder, new generalizations of Hermite-Hadamard inequality are obtained. Many reduced corollaries about the main findings are presented for classical integrals.

scholarly journals Fractional Integral Inequalities via Atangana-Baleanu Operators for Convex and Concave Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ahmet Ocak Akdemir ◽  
Ali Karaoğlan ◽  
Maria Alessandra Ragusa ◽  
Erhan Set
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Concave Functions ◽  
Fractional Operators ◽  
Fractional Integral Operators

Recently, many fractional integral operators were introduced by different mathematicians. One of these fractional operators, Atangana-Baleanu fractional integral operator, was defined by Atangana and Baleanu (Atangana and Baleanu, 2016). In this study, firstly, a new identity by using Atangana-Baleanu fractional integral operators is proved. Then, new fractional integral inequalities have been obtained for convex and concave functions with the help of this identity and some certain integral inequalities.

scholarly journals FRACTIONAL INTEGRAL OPERATORS IN NONHOMOGENEOUS SPACES

2009 ◽  
Vol 80 (2) ◽  
pp. 324-334 ◽  
Author(s):  
H. GUNAWAN ◽  
Y. SAWANO ◽  
I. SIHWANINGRUM
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Type Inequality ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Homogeneous Type ◽  
Fractional Integral Operators

AbstractWe discuss here the boundedness of the fractional integral operatorIαand its generalized version on generalized nonhomogeneous Morrey spaces. To prove the boundedness ofIα, we employ the boundedness of the so-called maximal fractional integral operatorIa,κ*. In addition, we prove an Olsen-type inequality, which is analogous to that in the case of homogeneous type.

scholarly journals Some Inequalities of Generalized p-Convex Functions concerning Raina’s Fractional Integral Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Changyue Chen ◽  
Muhammad Shoaib Sallem ◽  
Muhammad Sajid Zahoor
Keyword(s):  
Integral Operator ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Applied Mathematics ◽  
Optimization Theory ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Fractional Integral Operators

Convex functions play an important role in pure and applied mathematics specially in optimization theory. In this paper, we will deal with well-known class of convex functions named as generalized p-convex functions. We develop Hermite–Hadamard-type inequalities for this class of convex function via Raina’s fractional integral operator.

scholarly journals Some estimations on continuous random variables for (k, s) −fractional integral operators

2020 ◽  
Vol 6 (1) ◽  
pp. 143-154
Author(s):  
Mohamed Houas
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Random Variables ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integral Operators

AbstractIn this work, we establish some new (k, s) −fractional integral inequalities of continuous random variables by using the (k, s) −Riemann-Liouville fractional integral operator.

scholarly journals Sharp Weighted Bounds for Fractional Integral Operators in a Space of Homogeneous Type

2014 ◽  
Vol 114 (2) ◽  
pp. 226 ◽  
Author(s):  
Anna Kairema
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Operator Norm ◽  
Fractional Integral Operator ◽  
Weighted Spaces ◽  
Space Of Homogeneous Type ◽  
Homogeneous Type ◽  
Fractional Integral Operators ◽  
The Relationship

We consider a version of M. Riesz fractional integral operator on a space of homogeneous type and show an analogue of the well-known Hardy-Littlewood-Sobolev theorem in this context. In our main result, we investigate the dependence of the operator norm on weighted spaces on the weight constant, and find the relationship between these two quantities. It it shown that the estimate obtained is sharp in any given space of homogeneous type with infinitely many points. Our result generalizes the recent Euclidean result by Lacey, Moen, Pérez and Torres [21].

scholarly journals Chebyshev type inequalities involving generalized Katugampola fractional integral operators

2019 ◽  
Vol 50 (4) ◽  
pp. 381-390 ◽  
Author(s):  
Erhan Set ◽  
Junesang Choi ◽  
\.{I}lker Mumcu
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Research Subjects ◽  
Fractional Integral Operators ◽  
Katugampola Fractional Integral

A number of Chebyshev type inequalities involving various fractional integral operators have, recently, been presented.Here, motivated essentially by the earlier works and their applications in diverse research subjects, we aim to establish several Chebyshev type inequalities involving generalized Katugampola fractional integral operator. Relevant connections of the results presented here with those (known and new) involving relatively simpler and familiar fractional integral operators are also pointed out.

scholarly journals Some new generalizations of Ostrowski type inequalities for s-convex functions via fractional integral operators

Filomat ◽  
2018 ◽  
Vol 32 (16) ◽  
pp. 5595-5609
Author(s):  
Erhan Set
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Fractional Integral ◽  
Present Note ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Class Of Functions

Remarkably a lot of Ostrowski type inequalities involving various fractional integral operators have been investigated by many authors. Recently, Raina [34] introduced a new generalization of the Riemann-Liouville fractional integral operator involving a class of functions defined formally by F? ?,?(x)=??,k=0 ?(k)/?(?k + ?)xk. Using this fractional integral operator, in the present note, we establish some new fractional integral inequalities of Ostrowski type whose special cases are shown to yield corresponding inequalities associated with Riemann-Liouville fractional integral operators.

scholarly journals Fractional calculus pertaining to multivariable Aleph-function

2022 ◽  
Vol 40 ◽  
pp. 1-10
Author(s):  
Dinesh Kumar ◽  
Frederic Ayant
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
General Class ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
General Nature ◽  
Fractional Integral Operators ◽  
Mellin Transforms ◽  
General Class Of Polynomials

In this paper we study a pair of unied and extended fractional integral operator involving the multivariable Aleph-function, Aleph-function and general class of polynomials. During this study, we establish ve theorems pertaining to Mellin transforms of these operators. Furthers, some properties of these operators have also been investigated. On account of the general nature of the functions involved herein, a large number of (known and new) fractional integral operators involved simpler functions can also be obtained . We will quote the particular case concerning the multivariable I-function dened by Sharma and Ahmad [20] and the I-function of one variable dened by Saxena [13].

scholarly journals Fractional calculus pertaining to multivariable I-function defined by Prathima

2019 ◽  
Vol 15 (2) ◽  
pp. 61-73
Author(s):  
D. Kumar ◽  
F. Y. Ayant
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
General Class ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
General Nature ◽  
Fractional Integral Operators ◽  
Mellin Transforms

Abstract In this paper, we study a pair of unified and extended fractional integral operator involving the multivariable I-functions and general class of multivariable polynomials. Here, we use Mellin transforms to obtain our main results. Certain properties of these operators concerning to their Mellin-transforms have been investigated. On account of the general nature of the functions involved herein, a large number of known (may be new also) fractional integral operators involved simpler functions can be obtained. We will also quote the particular case of the multivariable H-function.

scholarly journals Some new extensions for fractional integral operator having exponential in the kernel and their applications in physical systems

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 478-491 ◽  
Author(s):  
Saima Rashid ◽  
Dumitru Baleanu ◽  
Yu-Ming Chu
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Circuit Theory ◽  
Future Research ◽  
Fractional Operators ◽  
Fractional Integral Operators ◽  
Physical Systems ◽  
Increasing Functions ◽  
Harmonically Convex Functions

AbstractThe key purpose of this study is to suggest a new fractional extension of Hermite–Hadamard, Hermite–Hadamard–Fejér and Pachpatte-type inequalities for harmonically convex functions with exponential in the kernel. Taking into account the new operator, we derived some generalizations that capture novel results under investigation with the aid of the fractional operators. We presented, in general, two different techniques that can be used to solve some new generalizations of increasing functions with the assumption of convexity by employing more general fractional integral operators having exponential in the kernel have yielded intriguing results. The results achieved by the use of the suggested scheme unfold that the used computational outcomes are very accurate, flexible, effective and simple to perform to examine the future research in circuit theory and complex waveforms.

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