Abstract Simpson inequalities for differentiable convex functions and their fractional versions have been studied extensively. type twice are also investigated. More precisely, Budak et al. established the first result on inequality functions. In present article, we prove a new identity addition to this, establish several whose second derivatives in absolute value convex. This paper is version of

The present paper first establishes that an identity involving generalized fractional integrals is proved for differentiable functions by using two parameters. By utilizing this identity, we obtain several parameterized inequalities the whose derivatives in absolute value are convex. Finally, show our main reduce to Ostrowski type inequalities, Simpson and trapezoid which earlier published papers.

We establish some Newton's type inequalities in the case of differentiable convex functions through well-known Riemann–Liouville fractional integrals. Furthermore, we give an example with graph and present validity newly obtained inequalities. Finally, for bounded variation.

Abstract In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using established identity, offer inequalities co-ordinated convex functions with a rectangle in plane $\mathbb{R} ^{2}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>R</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math> . Furthermore, by special choice of parameters our main results, obtain several...

We derive an identity for twice-differentiable functions whose second derivatives are convex. By using this equality, we establish some perturbed Newton type inequalities convex functions, which investigate by Riemann–Liouville fractional integrals. Furthermore, present our results special cases of the obtained theorems.

International Journal of Geometric Methods in Modern PhysicsAccepted Papers No AccessAdvancements Hermite–Hadamard Inequalities via Conformable Fractional Integrals for Subadditive FunctionsWali Haider, Huseyin Budak, Asia Shehzadi, Fatih Hezenci, and Haibo ChenWali Budak Search more papers by this author , Shehzadi Hezenci Chenhttps://orcid.org/0000-0002-9868-7079 https://doi.org/10.1142/S0219887825500999Cited by:0 (Source: Crossref) PreviousNext AboutFiguresReferencesRelatedDetailsPDF/EPUB...

This study presents novel formulations of fractional integral inequalities, formulated using generalized operators and the exploration convexity properties. A key identity is established for twice-differentiable functions with absolute value their second derivative being convex. Using this identity, several Hermite–Hadamard-type inequalities are developed. These extend classical midpoint trapezoidal-type while offering new perspectives through Also, some special cases align known results, an...

Inequalities involving fractional operators have also been an active area of research. These inequalities play a crucial role in establishing bounds, estimates, and stability conditions for solutions to integrals. In this paper, firstly we establish these new identities the case twice differentiable functions Caputo-Fabrizio By utilizing identities, novel are obtained trigonometric convex functions, exponential functions. It is expected that outcomes research will point developments study calculus.

From the past to present, various works have been dedicated Simpson’s inequality for differentiable convex functions. Simpson-type inequalities twice-differentiable functions subject of some research. In this paper, we establish a new generalized fractional integral identity involving functions, then use result prove Simpson’s-formula-type Furthermore, examine few special cases newly established and obtain several old inequalities. These types analytic inequalities, as well methodologies...

&lt;abstract&gt;&lt;p&gt;Fractional versions of Simpson inequalities for differentiable convex functions are extensively researched. However, type twice also investigated slightly. Hence, we establish a new identity functions. Furthermore, by utilizing generalized fractional integrals, prove several whose second derivatives in absolute value convex.&lt;/p&gt;&lt;/abstract&gt;

Abstract The authors propose a new method of investigation an integral identity according to conformable fractional operators. Moreover, some Newton-type inequalities are considered for differentiable convex functions by taking the modulus newly established equality. In addition, we prove several with aid Hölder and power-mean inequalities. Furthermore, results given using special choices obtained Finally, give bounded variation.

Simpson’s rule is a numerical method used for approximating the definite integral of function. In this paper, by utilizing mappings whose second derivatives are bounded, we acquire upper and lower bounds Simpson-type inequalities means Riemann–Liouville fractional operators. We also study special cases our main results. Furthermore, give some examples with graphs to illustrate This on first paper in literature as method.

Abstract In this current research, we focus on the domain of tempered fractional integrals, establishing a novel identity that serves as cornerstone our study. This paves way for Milne-type inequalities, which are explored through framework differentiable convex mappings inclusive integrals. The significance these in realm calculus is underscored by their ability to extend classical concepts into more complex, dimensions. addition, using Hölder inequality and power-mean inequality, acquire...

Abstract In this paper, we prove an equality for twice-differentiable convex functions involving the conformable fractional integrals. Moreover, several Bullen-type inequalities are established functions. More precisely, integrals used to derive such inequalities. Furthermore, sundry significant obtained by taking advantage of convexity, Hölder inequality, and power-mean inequality. Finally, provide our results using special cases theorems.

Abstract In the framework of tempered fractional integrals, we obtain a fundamental identity for differentiable convex functions. By employing this identity, derive several modifications Milne inequalities, providing novel extensions to domain integrals. The research comprehensively examines significant functional classes, including functions, bounded Lipschitzian and functions variation.

Abstract This paper investigates a technique that uses Riemann-Liouville fractional integrals to study several Euler-Maclaurin-type inequalities for various function classes. Afterwards, we provide our results by using special cases of obtained theorems and is derive examples. Moreover, give some bounded functions integrals. Furthermore, construct Lipschitzian functions. Finally, offer variation.

The authors of the paper present a method to examine some Newton‐type inequalities for various function classes using Riemann‐Liouville fractional integrals. Namely, are established by convex functions. In addition, several proved bounded functions Moreover, we construct Lipschitzian Furthermore, acquired integrals variation. Finally, provide our results special cases obtained theorems and examples.

In this article, we derive the above and below bounds for parameterized-type inequalities using Riemann–Liouville fractional integral operators limited second derivative mappings. These established generalized midpoint-type, trapezoid-type, Simpson-type, Bullen-type according to specific choices of parameter. Thus, a generalization many new results were obtained. Moreover, some examples obtained are given better understanding by reader. Furthermore, theoretical supported graphs in order...