Fractional Hermite-Hadamard Type Inequalities Research Articles

Some New Fractional Hermite-Hadamard type Inequalities For Generalized Class of Godunova-Levin Functions By Means of Interval Center-Radius OrderRelation with Applications

Some New Fractional Hermite-Hadamard type Inequalities For Generalized Class of Godunova-Levin Functions By Means of Interval Center-Radius OrderRelation with Applications

Fractional Hermite-Hadamard type inequalities for co-ordinated convex functions

In this paper, we first construct a new integral equality. Using this equality, we establish Hermite-Hadamard type fractional integralinequalities involving two variables via convexity.

Generalised Local Fractional Hermite-Hadamard Type Inequalities on Fractal Sets

Generalised Local Fractional Hermite-Hadamard Type Inequalities on Fractal Sets

Conformable fractional Hermite-Hadamard type inequalities for functions whose derivatives are s-preinvex

In this paper, we establish a new integral identity, based on this identity, we derive some new conformable fractional Hermite-Hadamard type inequalities for functions whose first derivatives are s-preinvex in the second sense.

Some new notions of fractional Hermite-Hadamard type inequalities involving applications to the physical sciences

The term convexity in the frame of fractional calculus is a well-established concept that has assembled significant attention in mathematics and various scientific disciplines for over a century. It offers valuable insights and results in diverse fields, along with practical applications due to its geometric interpretation. Moreover, convexity provides researchers with powerful tools and numerical methods for addressing extensive interconnected problems. In the realm of applied mathematics, convexity, particularly in relation to fractional analysis, finds extensive and remarkable applications. In this manuscript, we construct new fractional identities for differentiable preinvex functions to strengthen the recently assigned approach even more. Then utilizing these identities, some generalizations of the Hermite-Hadamard type inequality involving generalized preinvexities in the frame of fractional integral operator, namely Riemann-Liouville (R-L) fractional integrals are explored. Finally, we examined some applications to the q -digamma and Bessel functions via the established results. We used fundamental methods to arrive at our conclusions. We anticipate the techniques and approaches addressed by this study will further pique and spark the researcher's interest.

Some new fractional Hermite-Hadamard type inequalities for functions with co-ordinated extended [formula omitted]-prequasiinvex mixed partial derivatives

This article introduces extended (s,m)-prequasiinvex functions on coordinates, a new form of generalized convex function. Using a previously established identity, we derive new fractional Hermite-Hadamard type integral inequalities for functions whose mixed partial derivatives belong to this new class of functions. The obtained results generalize existing Hermite-Hadamard type inequalities and have numerous applications in mathematics and physics. To demonstrate the utility of our findings, we provide examples of applications to special means, such as arithmetic, harmonic and p-logarithmic means.

Some New Hermite–Hadamard Type Inequalities Pertaining to Generalized Multiplicative Fractional Integrals

There is significant interaction between the class of symmetric functions and other types of functions. The multiplicative convex function class, which is intimately related to the idea of symmetry, is one of them. In this paper, we obtain some new generalized multiplicative fractional Hermite–Hadamard type inequalities for multiplicative convex functions and for their product. Additionally, we derive a number of inequalities for multiplicative convex functions related to generalized multiplicative fractional integrals utilising a novel identity as an auxiliary result. We provide some examples for the appropriate selections of multiplicative convex functions and their graphical representations to verify the authenticity of our main results.

Certain inequalities in frame of the left-sided fractional integral operators having exponential kernels

<abstract><p>By virtue of the left-sided fractional integral operators having exponential kernels, proposed by Ahmad et al. in [J. Comput. Appl. Math. 353:120-129, 2019], we create the left-sided fractional Hermite–Hadamard type inequalities for convex mappings. Moreover, to study certain fractional trapezoid and midpoint type inequalities via the differentiable convex mappings, two fractional integral identities are proven. Also, we show the important connections of the derived outcomes with those classical integrals clearly. Finally, we provide three numerical examples to verify the correctness of the presented inequalities that occur with the variation of the parameter $ \mu $.</p></abstract>

Fractional Hermite-Hadamard type inequalities for subadditive functions

In this paper, we establish different variants of fractional Hermite-Hadamard inequalities for subadditive functions via Riemann-Liouville fractional integrals. Moreover, we offer some fractional integral inequalities for the product of two subadditive functions via Riemann-Liouville fractional integrals. It is also shown that the inequalities offered in this research are the generalization of the already given inequalities for convex functions and subadditive functions.

Hermite–Hadamard-Type Inequalities for F -Convex Functions via Katugampola Fractional Integral

This article is organized as follows: First, definitions, theorems, and other relevant information required to obtain the main results of the article are presented. Second, a new version of the Hermite–Hadamard inequality is proved for the F-convex function class using a fractional integral operator introduced by Katugampola. Finally, new fractional Hermite–Hadamard-type inequalities are given with the help of F-convexity.

Conformable fractional Hermite-Hadamard type inequalities for product of two harmonic 𝑠-convex functions

In this paper, we establish some conformable fractional Hermite-Hadamard type integral inequalities via harmonic s s -convexity, and the estimates of the products of two harmonic s s -convex functions are also considered.

Fractional Hermite–Hadamard type integral inequalities for functions whose modulus of the mixed derivatives are co-ordinated $$(log,(\alpha ,m))$$-preinvex

In this paper, the concept of co-ordinated (log, (s, m))-preinvex functions is introduced. Some new fractional Hermite–Hadamard type inequalities based on new integral identity are established.

On some new fractional Hermite-Hadamard type inequalities for convex and co-ordinated convex functions

In this study, some new inequalities of Hermite-Hadamard type for convex and co-ordinated convex functions via Riemann-Liouville fractional integrals are derived. It is also shown that the results obtained in this paper are the extension of some earlier ones.

Generalized Fractional Hermite-Hadamard Type Inequalities for Convex Function

Generalized Fractional Hermite-Hadamard Type Inequalities for Convex Function

Some Fractional Hermite–Hadamard Type Inequalities for Interval-Valued Functions

In this paper, firstly we prove the relationship between interval h-convex functions and interval harmonically h-convex functions. Secondly, several new Hermite–Hadamard type inequalities for interval h-convex functions via interval Riemann–Liouville type fractional integrals are established. Finally, we obtain some new fractional Hadamard–Hermite type inequalities for interval harmonically h-convex functions by using the above relationship. Also we discuss the importance of our results and some special cases. Our results extend and improve some previously known results.

The right Riemann–Liouville fractional Hermite–Hadamard type inequalities derived from Green’s function

The purpose of this work is to present the right Riemann–Liouville fractional integral version of Hermite–Hadamard inequality via a relatively new method through the Green’s function approach. In the process, some identities are established. Using these identities, we obtain loads of new results for functions whose second derivative is convex, monotone, and concave in absolute value. We anticipate that the method outlined in this article will stimulate further investigation in this direction.

General inequalities related Hermite-Hadamard inequality for generalized fractional integrals

In this article, we first establish a new general integral identity for differentiable functions with the help of generalized fractional integral operators introduced by Raina raina and Agarwal et al. agarwal . As a second, by using this identity we obtain some new fractional Hermite-Hadamard type inequalities for functions whose absolute values of first derivatives are convex. Relevant connections of the results presented here with those involving Riemann-Liouville fractional integrals are also pointed out.

Fractional Hermite-Hadamard Type Inequalities for Functions Whose Derivatives are s-Preinvex

In this paper, we establish a new fractional integral identity, and then wederive some new fractional Hermite-Hadamard type inequalities for functionswhose derivatives are s-preinvex.

The left Riemann-Liouville fractional Hermite-Hadamard type inequalities for convex functions

Abstract In this paper, with a new approach, a new fractional Hermite-Hadamard type inequalities for convex functions is obtained by using only the left Riemann-Liouville fractional integral. Also, to have new fractional trapezoid and midpoint type inequalities for the differentiable convex functions, two new equalities are proved. Our results generalize earlier studies. We expect that this study will be lead to the new fractional integration studies for Hermite-Hadamard type inequalities.

Fractional Hermite-Hadamard type inequalities for co-ordinated prequasiinvex functions

Abstract Some new Ostrowski’s inequalities for functions whose n-th derivatives are h-convex are established.