scholarly journals Some Bullen-type inequalities for conformable fractional integrals

2020 ◽  
Vol 28 (2) ◽  
pp. 3-17
Author(s):  
Musa Çakmak
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Differentiable Functions ◽  
Type Integral

AbstractIn this study, the author has established a new lemma and Bullen-type inequalities for conformable fractional integrals. Also, it is given some applications involving Bullen type integral inequalities for differentiable functions to show the results.

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.

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.

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.

scholarly journals New Hermite-Hadamard-Fejér inequalities via k-fractional integrals for differentiable generalized nonconvex functions

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2549-2558
Author(s):  
Artion Kashuri ◽  
Themistocles Rassias
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Nonconvex Functions ◽  
New Class ◽  
Differentiable Functions ◽  
Special Cases

The authors discover a new interesting generalized identity concerning differentiable functions via k-fractional integrals. By using the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard-Fej?r type inequalities via k-fractional integrals for a new class of function involving Raina?s function, the so-called generalized (h1, h2)-nonconvex are presented. These inequalities have some connections with known integral inequalities. Also, some new special cases are provided as well from main results.

scholarly journals Different type parameterized inequalities via generalized integral operators with applications

2021 ◽  
Vol 66 (3) ◽  
pp. 423-440
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Integral Operator ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Erentiable Function ◽  
Almost All

"The authors have proved an identity for a generalized integral operator via di erentiable function with parameters. By applying the established identity, the generalized trapezium, midpoint and Simpson 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 identi ed. Some applications of presented results to special means and new error estimates for the trapezium and midpoint quadrature formula have been analyzed. The ideas and techniques of this paper may stimulate further research in the eld of integral inequalities."

Generalization of different type integral inequalities for generalized (𝑠, 𝑚)-preinvex Godunova–Levin functions

2018 ◽  
Vol 24 (2) ◽  
pp. 211-221
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Fractional Integral ◽  
Beta Function ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Type Integral

Abstract In the present paper, the notion of generalized {(s,m)} -preinvex Godunova–Levin function of second kind is introduced, and some new integral inequalities involving generalized {(s,m)} -preinvex Godunova–Levin functions of second kind along with beta function are given. By using a new identity for fractional integrals, some new estimates on generalizations of Hermite–Hadamard, Ostrowski and Simpson type inequalities for generalized {(s,m)} -preinvex Godunova–Levin functions of second kind via Riemann–Liouville fractional integral are established.

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.

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