scholarly journals New Modified Conformable Fractional Integral Inequalities of Hermite–Hadamard Type with Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Thabet Abdeljawad ◽  
Pshtiwan Othman Mohammed ◽  
Artion Kashuri
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Special Means ◽  
Conformable Fractional Integral ◽  
Fractional Parameter

In this study, a few inequalities of Hermite–Hadamard type are constructed via the conformable fractional operators so that the normal version is recovered in its limit for the conformable fractional parameter. Finally, we present some examples to demonstrate the usefulness of conformable fractional inequalities in the context of special means of the positive numbers.

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 The analytical solution of Van der Pol and Lienard differential equations within conformable fractional operator by retarded integral inequalities

2019 ◽  
Vol 52 (1) ◽  
pp. 204-212 ◽  
Author(s):  
Fuat Usta ◽  
Mehmet Zeki Sarıkaya
Keyword(s):  
Differential Equations ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Integral Inequalities ◽  
Fractional Operator ◽  
Van Der Pol ◽  
Global Existence Of Solutions ◽  
Explicit Bounds ◽  
Fractional Differential ◽  
Conformable Fractional Integral

AbstractIn this study we introduced and tested retarded conformable fractional integral inequalities utilizing non-integer order derivatives and integrals. In line with this purpose, we used the Katugampola type conformable fractional calculus which has several practical properties. These inequalities generalize some famous integral inequalities which provide explicit bounds on unknown functions. The results provided here had been implemented to the global existence of solutions to the conformable fractional differential equations with time delay.

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.

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.

New k-Conformable Fractional Integral Inequalities

2020 ◽  
pp. 35-47
Author(s):  
Muhammad Uzair Awan ◽  
Muhammad Aslam Noor ◽  
Sadia Talib ◽  
Khalida Inayat Noor ◽  
Themistocles M. Rassias
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Conformable Fractional Integral

Conformable fractional integral inequalities for some convex functions

2018 ◽  
Vol 27 (2) ◽  
pp. 207-213
Author(s):  
ERHAN SET ◽  
◽  
BARIS CELIK ◽  
ABDURRAHMAN GOZPINAR ◽  
◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Conformable Fractional Integral

The main purpose of this paper is to present new Hermite-Hadamard’s type inequalities for functions that belongs to the classes of Q(I), P(I), SX(h, I) and r-convex via conformable fractional integrals . The results presented here would provide extensions of those given in earlier works

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.

scholarly journals New Conformable Fractional Integral Inequalities of Hermite–Hadamard Type for Convex Functions

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 263 ◽  
Author(s):  
Pshtiwan Mohammed ◽  
Faraidun Hamasalh
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Conformable Fractional Integral ◽  
New Inequalities

In this work, we established new inequalities of Hermite–Hadamard type for convex functions via conformable fractional integrals. Through the conformable fractional integral inequalities, we found some new inequalities of Hermite–Hadamard type for convex functions in the form of classical integrals.

scholarly journals Some modifications in conformable fractional integral inequalities

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Dumitru Baleanu ◽  
Pshtiwan Othman Mohammed ◽  
Miguel Vivas-Cortez ◽  
Yenny Rangel-Oliveros
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Conformable Fractional Integral

scholarly journals Some Novel Fractional Integral Inequalities over a New Class of Generalized Convex Function

2022 ◽  
Vol 6 (1) ◽  
pp. 42
Author(s):  
Soubhagya Kumar Sahoo ◽  
Muhammad Tariq ◽  
Hijaz Ahmad ◽  
Bibhakar Kodamasingh ◽  
Asif Ali Shaikh ◽  
...  
Keyword(s):  
Applied Sciences ◽  
Fractional Integral ◽  
Bessel Functions ◽  
Fractional Operators ◽  
Modified Bessel Functions ◽  
New Class ◽  
Special Means ◽  
Special Cases ◽  
Related Integral ◽  
Increasing Function

The comprehension of inequalities in convexity is very important for fractional calculus and its effectiveness in many applied sciences. In this article, we handle a novel investigation that depends on the Hermite–Hadamard-type inequalities concerning a monotonic increasing function. The proposed methodology deals with a new class of convexity and related integral and fractional inequalities. There exists a solid connection between fractional operators and convexity because of its fascinating nature in the numerical sciences. Some special cases have also been discussed, and several already-known inequalities have been recaptured to behave well. Some applications related to special means, q-digamma, modified Bessel functions, and matrices are discussed as well. The aftereffects of the plan show that the methodology can be applied directly and is computationally easy to understand and exact. We believe our findings generalise some well-known results in the literature on s-convexity.

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