The principal motivation of this paper is to establish a new integral equality related k-Riemann Liouville fractional operator. Employing equality, we present several inequalities for twice differentiable convex functions that are associated with Hermite–Hadamard inequality. Additionally, some novel cases the established results different kinds derived. This sums up Riemann–Liouville and Hermite–Hadamard’s inequality, which have symmetric property. Scientific nature and, particularly,...

Abstract In this article, the notion of interval-valued preinvex functions involving Riemann–Liouville fractional integral is described. By applying this, some new refinements Hermite–Hadamard inequality for operator are presented. Some novel special cases presented results discussed as well. Also, examples to validate our results. The established outcomes article may open another direction different types inequalities functions, fuzzy and their associated optimization problems.

In this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type via new fractional integral operator associated with the Caputo–Fabrizio derivative are presented. Furthermore, identity for differentiable convex functions of first order is proved. Then, taking into account as an auxiliary result assistance Hölder, power-mean, Young, Jensen inequality, some estimations Hermite-Hadamard (H-H) type refinements Applications to special means trapezoidal quadrature...

In this paper, we propose some generalized integral inequalities of the Raina type depicting Mittag–Leffler function. We introduce and explore idea s-type convex function type. Based on this, discuss its algebraic properties establish novel version Hermite–Hadamard inequality. Furthermore, to improve our results, two new equalities, employing these present refinements Hermite–Hadamard-type A few remarkable cases are discussed, which can be seen as valuable applications. Applications...

The comprehension of inequalities in convexity is very important for fractional calculus and its effectiveness many applied sciences. In this article, we handle a novel investigation that depends on the Hermite–Hadamard-type concerning monotonic increasing function. proposed methodology deals with new class related integral inequalities. There exists solid connection between operators because fascinating nature numerical Some special cases have also been discussed, several already-known...

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

Recently, fractional calculus has been the center of attraction for researchers in mathematical sciences because its basic definitions, properties and applications tackling real-life problems. The main purpose this article is to present some integral inequalities Ostrowski type a new class convex mapping. Specifically, n–polynomial exponentially s–convex via operator are established. Additionally, we Hermite–Hadamard inequality. Some special cases results discussed as well. Due nature...

<abstract><p>The aim of this research is to combine the concept inequalities with fractional integral operators, which are focus attention due their properties and frequency usage. By using a novel operator that has an exponential function in its kernel, we establish new Hermite-Hadamard type inequality for LR-convex interval-valued function. We also prove fractional-order variants Fejér Pachpatte setting pseudo-order relations. showing several numerical examples, further...

Pisciculture significantly contributes to food security, nutrition, and rural livelihood in India, the world's second-largest fish producer. Odisha, with its abundant aquatic resources, offers immense potential for pisciculture, particularly districts like Puri, where it serves as a critical activity. However, socio-economic attributes of farmers, such education, income, resource access, remain inadequately explored, posing challenges sustainable development this sector. With background,...

In this paper, we define and investigate generalized exponential type convex functions namely exponentially $s$--convex function. the support of newly introduced idea, attain algebraic properties function, furthermore, in frame simple calculus, explore novel kind Ostrowski inequalities.

In this article, first, we deduce an equality involving the Atangana–Baleanu (AB)-fractional integral operator. Next, employing equality, present some novel generalization of Ostrowski type inequality using Hölder inequality, power-mean Young’s and Jensen for convexity |Υ|. We also deduced new special cases from main results. There exists a solid connection between fractional operators because their fascinating properties in mathematical sciences. Scientific inequalities nature and,...

In this study, we focus on the newly introduced concept of LR-convex interval-valued functions to establish new variants Hermite–Hadamard (H-H) type and Pachpatte inequalities for Riemann–Liouville fractional integrals. By presenting some numerical examples, also verify correctness results that have derived in paper. Because results, which are related differintegral ϱ1+ϱ22 type, novel context functions, believe will be a useful contribution motivating future research area.

The objective of this manuscript is to establish a link between the concept inequalities and Center-Radius order functions, which are intriguing due their properties widespread use. We introduce notion CR (Center-Radius)-order interval-valued preinvex function with help total relation two intervals. Furthermore, we discuss some new class preinvexity show that unifies several known concepts in literature also gives rise definitions. By applying these definitions, have amassed many classical...

Abstract In this investigation, we unfold the Jensen–Mercer ( $\mathtt{J-M}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>−</mml:mo> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> ) inequality for convex stochastic processes via a new fractional integral operator. The incorporation of processes, and operator having an exponential kernel brings direction to theory inequalities. With in mind, estimations Hermite–Hadamard–Mercer $\mathtt{H-H-M}$...

Many scholars have recently become interested in establishing integral inequalities using various known fractional operators. Fractional calculus has grown popularity as a result of its capacity to quickly solve real-world problems. First, we establish new the Hadamard–Mercer, Pachpatte–Mercer, and Dragomir–Agarwal–Mercer types containing an exponential kernel. In this regard, inequality proved by Jensen Mercer plays major role our main results. Integral involving convexity wide range...

&lt;abstract&gt;&lt;p&gt;Fractional operators with integral inequalities have attracted the interest of several mathematicians. Fractional are best utilized in mathematical science their features and wide range applications optimization, modeling, engineering artificial intelligence. In this article, we consider new variants Simpson-Mercer type involving Atangana-Baleanu (A-B) fractional operator for $ s $-convex functions. First, an identity, which acts as auxiliary result main results is...

&lt;abstract&gt;&lt;p&gt;In this paper, we proposed some new integral inequalities for subadditive functions and the product of functions. Additionally, a novel identity was established number Hermite-Hadamard type pertinent to tempered fractional integrals were proved. Finally, support major results, provided several examples corresponding graphs newly inequalities.&lt;/p&gt;&lt;/abstract&gt;

The theory of convexity plays an important role in various branches science and engineering.The main objective this work is to introduce the idea a generalized convex function by unifying s-type m-convex Raina type function.In addition, some beautiful algebraic properties examples are discussed.Applying new definition, we explore sort Hermite-Hadamard inequality.Furthermore, enhance paper investigate several estimations inequality.The concepts tools may invigorate revitalize for additional...

&lt;abstract&gt;&lt;p&gt;This paper deals with introducing and investigating a new convex mapping namely, $ n $-polynomial exponentially s $-convex. Here, we present some algebraic properties logical examples to validate the theory of newly introduced convexity. Some novel adaptations well-known Hermite-Hadamard Ostrowski type inequalities for this function have been established. Additionally, special cases established results are derived as well. Finally, applications limits means positive...

&lt;abstract&gt;&lt;p&gt;Defining new fractional operators and employing them to establish well-known integral inequalities has been the recent trend in theory of mathematical inequalities. To take a step forward, we present novel versions Hermite-Hadamard type for operator, which generalizes some operators. Moreover, midpoint identity is derived differentiable mappings, whose absolute value first-order derivatives are convex functions. considering this as an auxiliary result, several...

This research focuses on the Ostrowski–Mercer inequalities, which are presented as variants of Jensen’s inequality for differentiable convex functions. The main findings were effectively composed functions and their properties. results directed by Riemann–Liouville fractional integral operators. Furthermore, using special means, q-digamma modified Bessel functions, some applications acquired obtained.

In this investigation, the exact solutions of variable coefficients generalized Zakharov-Kuznetsov (ZK) equation and Gardner are studied with help an extended <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"><mfenced open="(" close=")"><mrow><msup><mrow><mi>G</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>/</mo><mi>G</mi></mrow></mfenced></math> expansion method. The main objective study is to establish closed-form dynamics analytical ZK equation. govern behavior nonlinear wave...

The class of symmetric function interacts extensively with other types functions. One these is the convex functions, which closely related to theory symmetry. In this paper, we obtain some new fractional Hermite–Hadamard inequalities an exponential kernel for subadditive functions and their product, known results are recaptured. Moreover, using a identity as auxiliary result, deduce several pertaining integrals involving kernel. To validate accuracy our results, offer examples suitable...

The main objective of this paper is basically to acquire some new extensions Ostrowski type inequalities for the function whose first derivatives' absolute value are $s$--type $p$--convex. We initially presented a auxiliary definition namely $p$--convex function. Some beautiful algebraic properties and examples related newly introduced discussed. additionally investigated cases that can be derived from novel refinements paper. These results yield us generalizations prior results. trust...

&lt;abstract&gt;&lt;p&gt;In this paper, using positive symmetric functions, we offer two new important identities of fractional integral form for convex and harmonically functions. We then prove variants the Hermite-Hadamard-Fejér type inequalities as well functions via integrals involving an exponential kernel. Moreover, also present improved versions midpoint Hermite-Hadamard inequality. Graphical representations are given to validate accuracy main results. Finally, applications associated...