New integral inequalities of Hermite–Hadamard type via the Katugampola fractional integrals for strongly $$\eta$$-quasiconvex functions

2020 ◽  
Author(s):  
Seth Kermausuor ◽  
Eze R. Nwaeze
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Quasiconvex Functions

scholarly journals Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications

2021 ◽  
Vol 5 (3) ◽  
pp. 80
Author(s):  
Hari Mohan Srivastava ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Dumitru Baleanu ◽  
Y. S. Hamed
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Wright Function ◽  
Nonconvex Functions ◽  
Special Cases ◽  
Type Integral ◽  
Generic Class ◽  
Two Parameters ◽  
Class Of Functions

In this paper, the authors define a new generic class of functions involving a certain modified Fox–Wright function. A useful identity using fractional integrals and this modified Fox–Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite–Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.

Fractional quantum integral operator with general kernels and applications

2017 ◽  
Vol 20 (01) ◽  
pp. 1750003
Author(s):  
Azizollah Babakhani ◽  
Abdolali Neamaty ◽  
Milad Yadollahzadeh ◽  
Hamzeh Agahi
Keyword(s):  
Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Fractional Quantum ◽  
Quantum Integral

In this paper, we first introduce the concept of fractional quantum integral with general kernels, which generalizes several types of fractional integrals known from the literature. Then we give more general versions of some integral inequalities for this operator, thus generalizing some previous results obtained by many researchers.2,8,25,29,30,36

scholarly journals Fractional trapezium type inequalities for twice differentiable preinvex functions and their applications

2020 ◽  
Vol 10 (2) ◽  
pp. 226-236
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Trapezium Type ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Preinvex Functions ◽  
Almost All

Trapezoidal inequalities for functions of divers natures are useful in numerical computations. The authors have proved an identity for a generalized integral operator via twice differentiable preinvex function. By applying the established identity, the generalized trapezoidal type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identified. Some applications of presented results to special means have been analyzed. The ideas and techniques of this paper may stimulate further research.

scholarly journals Fractional Hermite–Hadamard–Fejer Inequalities for a Convex Function with Respect to an Increasing Function Involving a Positive Weighted Symmetric Function

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1503 ◽  
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Artion Kashuri
Keyword(s):  
Fractional Calculus ◽  
Convex Function ◽  
Symmetric Function ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Fractional Operators ◽  
Important Direction ◽  
Increasing Function

There have been many different definitions of fractional calculus presented in the literature, especially in recent years. These definitions can be classified into groups with similar properties. An important direction of research has involved proving inequalities for fractional integrals of particular types of functions, such as Hermite–Hadamard–Fejer (HHF) inequalities and related results. Here we consider some HHF fractional integral inequalities and related results for a class of fractional operators (namely, the weighted fractional operators), which apply to function of convex type with respect to an increasing function involving a positive weighted symmetric function. We can conclude that all derived inequalities in our study generalize numerous well-known inequalities involving both classical and Riemann–Liouville fractional integral inequalities.

scholarly journals Some New Tempered Fractional Pólya-Szegö and Chebyshev-Type Inequalities with Respect to Another Function

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Gauhar Rahman ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad ◽  
Muhammad Samraiz
Keyword(s):  
Present Article ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Bounded Functions ◽  
New Inequalities

In this present article, we establish certain new Pólya–Szegö-type tempered fractional integral inequalities by considering the generalized tempered fractional integral concerning another function Ψ in the kernel. We then prove certain new Chebyshev-type tempered fractional integral inequalities for the said operator with the help of newly established Pólya–Szegö-type tempered fractional integral inequalities. Also, some new particular cases in the sense of classical tempered fractional integrals are discussed. Additionally, examples of constructing bounded functions are considered. Furthermore, one can easily form new inequalities for Katugampola fractional integrals, generalized Riemann–Liouville fractional integral concerning another function Ψ in the kernel, and generalized fractional conformable integral by applying different conditions.

Some new fractional integral inequalities for generalized relative semi-m-(r; h1, h2)-preinvex mappings via generalized Mittag-Leffler function

2019 ◽  
Vol 26 (1/2) ◽  
pp. 41-55 ◽  
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Invex Set ◽  
Special Means ◽  
Special Cases ◽  
Differentiable Mappings

The authors discover a new identity concerning differentiable mappings defined on m-invex set via fractional integrals. By using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized relative semi- m-(r;h1,h2)-preinvex mappings by involving generalized Mittag-Leffler function are presented. It is pointed out that some new special cases can be deduced from main results of the paper. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.

NEWTON’S-TYPE INTEGRAL INEQUALITIES VIA LOCAL FRACTIONAL INTEGRALS

Fractals ◽  
2020 ◽  
Vol 28 (03) ◽  
pp. 2050037 ◽  
Author(s):  
Sabah Iftikhar ◽  
Poom Kumam ◽  
Samet Erden
Keyword(s):  
Fractional Derivatives ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Quadrature Rules ◽  
Special Means ◽  
Type Integral

We firstly establish an identity involving local fractional integrals. Then, with the help of this equality, some new Newton-type inequalities for functions whose the local fractional derivatives in modulus and their some powers are generalized convex are obtained. Some applications of these inequalities for Simpson’s quadrature rules and generalized special means are also given.

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